AE (don't know LM or GL) is one of those programs which will happily make use of whatever iron (both CPU and RAM) you throw at it.
That being said, I've used it on far worse computers than you (iMac DVSE 400/256MB RAM), and it functions fine.
The more RAM the better though, AE really likes it. I mean REALLY likes it. RAM is cheap. Max it out.
1024x768 is pretty cramped but useable. How cramped depends on what you're doing. If you have an external preview set up, and are doing mostly filter work, 1024x768 is fine. For Complicated masking/roto kind of stuff, you'll work faster (and be happier) with more screen.
Lastly, did I say max out your memory? I'm not kidding here.
I love AE talk, so if you have more specific questions, I'd be glad to help!
[edit: removed stray word]