As the 2 above me said, you want a heavy horse. Destrier is nice because it is cheap and seems to handle better than the other "heavy" horses, but I prefer the Large Warhorse/Warhorse. They take a lot more hits from arrows and have near the same maneuver/speed stats. It does cost a bit so if money is something of an issue I would go Destrier base simply off that.
As far as the build is concerned you can go 21 or 24/15. 21 gives you the option to go more IF/WM or even Shield/Throwing if you want. I go for that extra Power Strike because it helps to 1 shot those plate wearing heroes. Also what helps is a pierce/blunt damage weapon. My personal choice is the Morningstar. Good speed, Awesome Damage and crappy range but you want to be close to infantry as little as possible and a cut damage weapon you will be going in once, twice or more.
For a budget build I would go 24/15 with Shortened Military Scythe (39 cut, stab attack when dismounted and the all important 112 reach) Rouncey and one of the tunics over mail (good body armor, decent leg armor).
When you have a multi or feel like going Rambo 24/15 With Morningstar Some sort of upgrade to the tunic over mail (I use Pronoia for it's awesome leg/body armors) and the Destrier or whatever you feel like paying.
Also here are some tips for playing I had posted in other threads a while back as far as the play style.
Post about 2h strats:
http://forum.meleegaming.com/beginner%27s-help-and-guides/bastard-on-a-horse/Post in a 2h cav build thread:
24/15
IF:5
PS:8
Athletics:5
Riding:5
All else:0
2h WPF:111(at 30)
Armor: Heavy body armor with good leg def. (40+ body and 13+ leg) and Good boots (spurs because you are cav duh). Whatever else you want
Horse: Destrier or above. Personal favore is Large Warhorse because you will be a HUGE arrow target and this thing soaks em up like a sponge.
Weapon(most important part of 2h cav): I can't believe this isn't more commonly used but the freakin Shortened Military Scythe. 112 range, 39 damage. Only downfall? It's slow.
Weapon(secondary): Great Maul for when you get dismounted or a Axe/Morningstar of your choice. The Scythe is still surpisingly good at dueling dismounted.
Strategy(beginning of round): Beginning of round I rush straight at the blob. Archers will predictibly shoot at you and infantry will chase you. Cav will be trying to couch you so the zig zag trot is essential. When you get the infantry seperates from the archers now you go get some work done. Archers die in 1-2 swings from the Scythe so take a few out and go treat your wounds.
Strategy(Mid round): Support your infantry with bumps and learn how to use manuevering to pwn Spear cav. Ctrl+J works against coursers, and against anything else just bait them to swing at you while evading where the swing will be last second. To really make a spear cav. look bad hold down block and intercept your horse to cut his off. He will thrust into your block, maybe damaging your horse but now he is in your range. You can stay pure infantry support and just protect infantry against cav + bump etc. Or you can be more offensive using the zig-zag trot effectively helps here. Archers are your bread and butter here, bait spearmen away like you do in the beginning game and take out archers.
Any questions?