I usually do most of my fighting during the Crusader, Archer/Musketeer stage of the game. If that doesn't drop the AI to one city I then usually use the Cannon on railroad/Riflemen combo. There's not anything left after that point, so I don't get to use Howie's or aircraft too much.
I usually play archipelago, so I use a large Navy, consisting of large numbers of fast ships, like destroyers. As for ground, I use a cavalry/diplomat aproach, where cavalry will attack cities, and the diplomats will bribe enemy units and destroy city walls in case of advanced defenses...
I rarely risk war earlier than that, because I take a while to settle down and build up my empire. Forts also are the main defesnes of my empire pre-air, they usually have more ground defense than my average cities, around 6 units in each. I'd rather my forts be destroyed than my cities.
Either Knights and crusaders>dragoons>cavalry.
Thats it.Nothing else is needed....although it can be fun to use engineers and artillery.Alpines and partisans/explorers.Pikes and catapults with pre-worked settlers is a methodical way to go.
Vet ironclads are tons o' fun.
I've never had much success with chariots or elephants...but I know plenty that have.Even horsemen can be effective if used early enough.
Early war has always seemed most logical to me as this is when the ai is at it's weakest.Once they get gunpowder,they tend to fill cities with muskets behind walls.This takes alot more resources to crack these cities(Bribing is no fun).If its on a river..well even vet cavs have a tough time.Thats where dips and artillery come into play.Even cannons..they hit hard.
City defence units in the main.
For outer offence, Marines, Armor etc, either bribed, or from ST city.
Earlier than that, only a few mobile troops, diplomats, and a small navy.
I do not do much fighting until the time suits me perfectly, ie modern era, and, if the truth be known, find it too boring and easy to take down the AI early. I prefer to let it grow nice and big, so I can actually have something to do later.
In the early stages of the game I expand my civilisation and usually take contro over a continent, which is very easy to defend. Usually I share the continent with one AI, and I move quickly to eliminate that opponent, but when that has been achieved I consolidate. In the beginning I always believe I can finish my consolidation within a couple of years, but when I reach a point where I feel ready to expand and absorb, without having to rely on the production of the new territories, I find myself with howitzers and stealth fighters...
First I use mainly legions and catapults, push them to the adjacent spots of an enemy city, and attacking after one turn.
Then I use the same technique when I acquire more advanced artillery units and infantry units.
Airplanes are rarely something I rely on, since bombers have only one strike per turn, and I need more attacks per unit to defeat the enemies at a very late point in the game.
Due to my policy of consolidation, I also build very much infrastructure, so a few artillery units positioned at a railroad crosspoint is enough to push any invasion into the sea immediately.
I build a large navy, due to the fact, that I control an entire continent. I do not build fast units, because they tend to be weaker than they're fast. Instead I rely on scattered submarines, and many large, heavy ships.
I usually do not begin expanding before I have achieved absolute superiority to the enemy. That way I can make 'blitzkrieg' and absorb an AI within a few turns.
I rarely conquer the world during the earlier ages unless i am going for the conquer-the-world to get a lot of points but you can't get as many points that way as the future tech-spaceship way. I don't like the units--too slow, AI's cities all have city walls. I am to busy building caravans and building trade so that i reach the modern age of aircraft while they still have muskateers. Then i build a huge invasion force, and since you usually only get like one turn where the senate isn't being stupid, i conquer an entire civilization all in one turn,or all except for their smallest city, with bombers and fighters, spys for city walls and tanks. Battleships are nice to have for coastal cities but not necessary.
To make it through the ages just make sure you have well defended cities near your enemies and the Great wall. If you have to take their cites early on, RR and cannon work okay.
Even WITH aircraft (which I don't use too much, except for fighters/stealth fighters for kamikaze runs against barb hordes) I usually have a variety. Supported by EACH CITY I have about: 3 Riflemen, 8 Marines (I garrison fortresses with them), 12 Armor, 8 Howitzers,2 Alpine Troops, 2 Engineers and 9 Mech. Inf. That'll do you through any war. In EACH coastal city, I also have about: 3 Destroyers, 5 Transports 1 Battleship, 2 Cruisers. Don't mess with me rival civs, or you WILL be flattened before you can say: Nuke incoming...