Depends on the unit - each one has different standard sizes. Short answer, 80 and 120, regulars and peasants. On a 2.5ghz-type system battles run nicely. I think that's regular or large size, but I forget if that's correct.
Regarding generals, 2 things to keep in mind, there are "command stars" and "valour experience" (the bronze/silver/gold chevrons").
Command stars are based on winning battles - just win lots of battles with the same general, especially when fighting outnumbered and crushing the enemy to get faster upgrades.
Second, there's the "valour experience" - pretty easy, but a little dangerous: send them into the fights to gain more experience - same way all units gain experience, really.
The danger, of course, is that he gets killed. But if you just let him hang around until it's time to mop up the retreating enemy the chance that he'll get a promotion is understandably lower.
Ideally, try and keep one or two extra cavalry units around to offer support in case the general gets stuck in a particularly nasty fight.
As for multiplayer, I haven't played much - but if I had to guess, I'd say 1. experiment and then 2. play with what works for you.
