I'd have to say, I agree on NVidia over ATI for compatibility alone. I've seen several forums where people outline which ATI driver versions work with which game, and frankly, it reads like a shopping list. "Drivers from 10.1 - 10.4 work for this game, this game works with 10.5 and up, this other game stopped working at 10.9..." I've
never had to roll back the drivers on my NVidia card, and I play games with a pretty wide selection of ages and video requirements. ATI may be superior in cost-versus-power, but that hardly matters if your drivers screw over half the games I want to play, does it?
On the other hand, I've heard lots of good things about AMD processors. The Intel vs AMD CPU debate is a lot like the Nvidia versus ATI GPU debate, where the former produces expensive, top-of-the-line devices and the latter produces slightly less-powerful, far cheaper devices. The difference is, AMD processors actually
work, whereas ATI GPUs often don't.
Cases really don't make much of a difference - if your case can actually
hold everything inside it, then you're set. Sure, there's a bunch of talk about 'airflow', but if you're really having airflow problems, remove the side of the case and replace it with a cheap mesh or something. It's certainly not worth spending a hundred bucks to slightly reduce heat, especially if you're not obsessively overclocking.