The assumption behind the issue of warring as a republic is that you are not playing a conquest / always warring game, rather you are playing some sort of builder game. This could be explicit (eg culture victory only) or implicit, by the strategy you have taken. The assumption is not always valid for instance if you are playing a religious civ, so anarchy is not a problem and you are at republic merely as a way of being out of despotism but it is a reasonable one.
Another assumption here is that we are looking at a war commencing at some stage from late-ancient on, since it is unlikely that you will have got republic before then. At this level individual units are reasonably balanced. Indeed, including terrain / fortification factors, the edge probably lies with defence in any 1:1 battle.
On this basis, warring is a means to an end, not an end in itself. You are going to war, either because you have been dragged into one, or because you need to. Ignoring wars initiated by the AI, why should you, as a republic go to war? If you need territory this early in the game, republic is the wrong government, as it is clear territory shortage is going to be a game-long problem. Whilst you can war the whole game in republic mode, the exercise is self-defeating. Equally civ destruction is a by-product of warring, not an aim.
So what reasons are there for going to war in republic mode? Most of the time, these revolve around resources and luxuries. You should war to a) get a resource you do not have (because of their uneven geographic distribution, oil and saltpetre are the two that come to the fore here). b) Split an AI civ from any military resource combo (iron / horses, horses / salterpeter and rubber / oil are the three key ones). c) Obtain a monopoly of a luxury or takeaway a monopoly. Luxury monopolies are extremely valuable in a builder game and are well worth fighting for. (You can get up to 200 gpt for the whole game from a luxury monopoly, well worth a 10 turn war on its own account, let alone the benefit of denying the AI the same opportunity. Getting a monopoly on uranium is often advisable.)
Having decided the reason for going to war, you need to assess how long the war will take to achieve your aim. A reasonable rule of thumb is one square per turn. So if the oil you need is 20 squares from your border, it will take you twenty turns. If the figure is over 20, you can and probably should sign up some alliances. You should align with all the countries on your border, to prevent them from aligning with the opposition, plus the odd far-away civ.
Next thing is preparation time. You probably need one turn for every two you intend to be at war in preparing your military build-up. During that time you need to complete all necessary buildings (temples and barracks are a must, market-places are useful, libraries are a bonus, granaries are unnecessary at this point whilst cathedrals are a necessity in cities with hospitals) and start work on your military.
Unlike democracy, you can wage war in republic for a very long period of time in terms of war weariness. What is hurting you during that time is upkeep on the army (480 units is 480gpt, the cost of rushing a temple each turn) and the shields / cash on rushing replacements, when you could be building universities etc. Indeed you want to keep the military down to below the gpt that you expect to earn from your conquest.
What you clearly want, therefore, is a large enough army to win, but equally importantly, one that does not take too many casualties. Basically, you want to build it up, send it into battle and watch it grind out victory after victory. Sending hundreds of cavalry to attack infantry in a city is fun initially, but excrutiating as you see red-lined cavs die against red-line infantry, which then upgrade and go yellow, and you realize that you are going to have to rush ten or fifteen new cav to advance.
The solution, of course, is bombardment. Bombarding units inflict damage to varying degrees, but dont sustain hits directly. Stacked with a handful of good defenders, they are close to unbeatable over time. However, you do need a lot of them at the beginning. In a given attack, assume that 25% of the barrage fails, 25% of the time an improvement is hit (until there are none left) and 25% of the time the population suffers. That means that a stack of 12 cannon etc are likely to knock just 3 points off the defenders until the improvements have been eliminated (at which point it rises to 6). These ratios change the smaller the city gets. So below size 7, with no improvements left, you are probably getting 8 hits.
This does not sound very good, but it is actually more than sufficient, over time. Assume that you have three veteran infantry defending a size 14 city with six improvements. Rounds one and two reduce the city size and eliminate improvements. Round three gets the city below size 7, so you get eight hits on three infantry, red-lining two of them. Given that you can only recoup 2 hits per unit per turn, that will leave two units at 3 / 4 level going into round 4. Another 8 hits in that round will leave all three units at 1 / 4. That is when you can go in and attack. You will be very unlucky if you lose a 4 / 4 cavalry in the attack, even though it is 6 : 10 + defensive bonus against you, because you would have to lose four straight random number roles, the odds of which are about 1 : 6. (This in turn means that you would expect to lose one cavalry unit every third city (assuming three infantry defending.)
On this basis, 12 seems a very good number of bombarding units. Catapults bombard at 4, cannon at 8 and artillery at 12 and all these are higher than the basic defensive levels of their expected opponents (muskets, rifles and infantry), so you get roughly the same degradation. Having sixteen may enable you to take the city in three turns, since you would be degrading the military from Turn 1 and is probably what you would need if you come across four defenders, but is considerably more expensive and in the scheme of things, one turn does not make a lot of difference.
Since bombarding units can not take a city, the number of offensive units in the division needs to at least equal the number of defenders. Given the chance of losing a unit, it makes sense to have slightly more. It also makes sense to have attacking units that have speed. This is so that once the battle is over you can send your bombarding units off to the next city and but give your attacking units time to recuperate, because they can move swiftly enough to catch up. You can have a rough idea about the number of defenders you are likely to face, but as a basic rule, you need three bombarding units for every offensive unit.
You do not need many defensive units in the stack, but it is worth remembering that you will be leaving defensive units behind when you take a city. On the assumption that you leave two per city, the number of defensive units you need is about half the number of turns you expect to fight. However, you do not need to have all these built immediately. If you start off with four, you should be able to replace them at a sensible rate.
All told, then, the basic division is 12x bombardment, 4x defence, 4x speed. In general this will attack one city. Depending on (1) the number of cities you have and (2) the complexity of the battle plan, you will need to have built between one and five of these divisions. It is quite possible that there are individual cities, which because of size or defensive features will require two divisions combining and later separating. You should plan your attack route accordingly.
As well as attacking divisions, you are going to need a home guard. At some point a serious opponent will send an SoD in. If an SoD takes one of your cities, it rapidly increases war weariness. It is vital therefore that you take out the SoD, which in turn means trapping it, which means building the military means to trap it.
It is best to assume an SoD of 30x units will come at you. Usually these are a bizarre mixture of obsolete and upgraded weaponry, but are pretty nasty in aggregate. If you are railroaded, all units have the same speed in your own country, but if you are just roaded, then you need to build a 30x knight / cavalry division. Once youve eliminated the SoD threat, you can dismantle this division and use it to guard your frontline cities. If a 50x SoD comes towards you, by attacking first assuming suitable firepower your 30x division should win but it will take a battering.
Depending on the complexity of the planned war, you should be looking at a minimum of a 50x army, probably 90x and plausibly 130x. Some of these units will already be in situ. However, almost certainly the bulk of the bombardment capability will not be. Having rushed to complete any necessary improvements, you need to build the army. Remember to build the bombardment capabilities in cities that do not have barracks and build the offensive capabilities in the cities further away from the front line. Fiscally, it makes sense to rush in the cities with low output, complete the build in the others.
Whilst you are preparing road / railroad your front line. You need to be able to move troops up and down at a speed faster than the enemy. You also want to road / railroad extensively the area between and around your trap city and the border. Whats your trap city? This is the border town which is relatively lightly defended. It needs to be four squares from the border (beware of diagonals) if the opponent has cavalry, three squares otherwise. Ideally, this should be slightly away from your main point of attack, so any bombardment division does not come head-to-head with the SoD.
Just prior to going to war you need to do the following. Equip your border towns, except for the trap city, where you leave just one unit. Move your knight / cavalry division to within defending distance of the trap city (not an issue if you are railroaded). Tie-up alliances with all your neighbours, if appropriate. Make sure you have no units in the forthcoming enemy territory (quite possibly they have culturally expanded their borders into yours and some of your troops are now on the wrong side). F4 the target to check the technology status, then F4 again and declare war.
When attacking with a bombardment division, usual rules apply. Attack from a high point, do not attack across a river (if at all possible). Do not get greedy and attack before you have completely red-lined the defences (the odds change dramatically when fighting a 2 / 4 compared to a 1 / 4 and worse, you could easily create a 3 / 5). When you have taken the city, leave behind any damaged units and two defensive units and move on to your next target.
If you are railroaded, it is quite possible to divert a bombardment division or two to deal with the SoD. If the SoD is a mixed generation force (and if the AI runs out of money to upgrade it will send warriors and the like into battle) you can bombard the higher-quality units if not down to red-line then to yellow. Since they are out in the open, it is pretty easy to destroy them after that, if not on your attack then on theirs.
Concentrate, though, on running the country. If youve got a tech lead, you must make sure you keep it. There is no point in having spent $$$$ when money actually means something, to get a tech lead, only to throw it away now. To this aim, make full use of the fact that city growth is not advisable, right now, so you have surplus citizens. Do not waste them as entertainers, turn them into taxmen. Indeed be wary of city growth, as disorder can be a problem.
Those cities, which have already completed their improvements, make sure that they have barracks and use them to replenish your military. Build defensive units, rather than speed units. If you are losing speed units in the war, you can replenish them from the increasingly irrelevant knight / cavalry division. There should not be a need to hurry any military production. In those high corruption cities, build workers. In high corruption cities in inhospitable areas, build barracks (and ultimately military).
If you playing vanilla, this method of warring does not produce many GLs, but you should get a couple. As a rule, I go for Army / Palace move / Improvement / Improvement, but this is both a subjective / contentious issue and also one governed by circumstances. More importantly, do not waste a GL, because you may not get another. It is better to have it hanging around, preventing you getting the chance of another GL, than wasting it on building a university. This is particularly true if you are close to achieving your military aim. If you currently have nothing better to do with it, but reckon that you should get another reasonably soon, armies are useful in this form of warfare as you would have to lose 12 random rolls in a row rather than 4, something you may need if you are attacking a town on a hill. (Still, I would prefer to hurry a military academy and use that to create armies, rather than use a GL.) Do remember to try to save a GL to build the UN. This is more important than Universal Suffrage. (Youve spent most of the game as a republic, why become a democracy now?)
I dont think that you need to treat acquired cities any differently in republic. Make sure that you do not raze any, since it hits your reputation. When fighting an equal civ, they will flip and there is very little you can do about this, other than make sure that you do not have too many troops in the city after the second turn. (If you have a 1 / 4 cavalry recuperating, move it outside the city when it is 3 / 4. It can get the additional point outside and if the city flips you can take it back quickly.) It makes sense to rush temples more for the city size factor than happiness. Whilst immoral, ethnic cleansing has its uses.
Once the war is over, there is a serious question of whether or not you should disband some or all of the army. Prior to modern times, it does not make sense to do this, in part because you can usually identify another military target to use your army on. However, if everyone is up to, say, combustion, cavalry is about to become, if not obsolete, then certainly sub-optimal. Scrapping most of the cavalry gets you a few shields, but more importantly will save over 30 gpt. It does not make sense to scrap artillery, since once you have railroaded, your artillery is an awesome defensive capability. (One of your long-time allies, upset at the increasingly huge gpt its paying you sends in a tank SoD only to watch it red-lined as you converge all your artillery on it.)
It's funny in the same way that newspaper comics can be funny when the captions are switched.
