GTA4's over-rated personally, bought it, played it for a bit and... It's like every other GTA -ever-. Good solid game but that's all. (Live may well be better) I'd always advise CoD4 as the first game you buy, the best game out at the moment to show what the 360 is capable off
pretty much the best games are either halo 3 if u like sci-fi or cod4 if u like military these will last a long time because live rarely gets boring on huge multiplayer games
If there's lag it can affect you really badly, you'll find the game to be unplayable half of the time, but that never really occurs unless it's yourself who has lag. Xbox Live usually runs smoothly. And like others have said you really should get GTA IV first The online play is best.
yeah I hardly ever have a problem with lag on live, resolves the problem better than PSN seen as you get what you pay for if you like FPS games also I would recommend along with CoD4, Battlefield: Bad Company