As a former monarchy/communism only player I must say that I've had great results in republic.
I am a warlike player and in the past I thought that monarchy/communism was the only way to go. Under those govts. you don't have to worry about war weariness or the high cost of maintaining a military. But one day I decided to try to play a peaceful game and made the early switch to republic instead of monarchy and boy what a difference! (Remember I am speaking from the point of view of a monarchy/communism only player)
I have successfully waged wars that lasted over 100 turns under republic! How you ask and more importantly why would you wage war for many many turns? Let me try to summarize for you how I go about doing it. I'm not saying that this is the only way to play the game. Just throwing out another perspective for you all to consider.
First off before making the switch to republic you must have at least 5-6 cities, in addition to the capital, at size 6 or greater. They must have relatively low corruption and must be producing lots of gold and science (i.e. markets, libraries, scientists, etc.) I usually make sure that they make at least 6-8 gold per turn and 10-14 science beakers. Furthermore make sure you have the Forbidden Palace in place. This greatly helps the cities around the one with the FP in it. Those cities don't necessarily have to have all the infrastructure in place. Finally make sure you have "mined" and "roaded" all the tiles that are grassland or hills next to the 5-6 cities. (see above posts regarding the additional benefits received from tiles that are producing at least one gold)
Ok so you have all the infrastructure in place so now what? Ask yourself this, do I have at least 4 luxuries coming in? You don't necessarily have to have them within your empire. You can trade for them. Making frequent fair trades with the AI, as well as giving gifts to him, will strengthen the relationship you have with those who have the goods your looking for. You want to make sure that you are guarenteed a steady trading partner or two.
Now you are ready to make the switch to republic. Go ahead and keep that big army too. You make more money in republic and with a little work prior to making the switch you should be operating in the "black" so to speak. Now notice how much faster you can research new techs for all those shiny new weapons? (I still play warlike even under republic but love the fact that I can still research new techs much faster than under monarchy and communism)
Before engaging in that long war make sure you have built the Suffrage wonder. It helps reduce war weariness. Eventually you want to have police stations in every major city in addition to all the happiness buildings of course. All this together with massive imports of luxuries should keep your ungrateful people quiet while you go and fight your monstrously long wars in peace. Why fight long wars? To keep the other civs out of republic and democracy so that you can overtake them in science. Hence why I like the benefits of science research under republic. War weariness is not as bad as under democracy another plus for republic! If you don't have "Suffrage" then don't worry, get more luxuries or now would be a good time to adjusts the science and luxury sliders. You should be ringing in the doe if you have the Wall Street minor wonder to be able to afford to give the whining masses some money so that you can wage your wars in peace. It is important to strangle and blast your enemies and keep them in war as long as possible while you advance down the tech tree. Make some MPP's if you like to tackle the big threats. Kill off the small enemy civs but if you can't eliminate the big boys keep them in war so that they'll have to switch out of democracy.
If you like to fight wars but are falling behind the tech race because you play only monarchy and communism then this advice may be of some use to you. It may not be the best approach to this game but for me, someone who loves to see wars and death and destruction done to my enemies, then give it a try!