You shouldn't really bother with graphic intensive games if you don't buy a laptop specifically for gaming. You can still play stuff like Plants vs Zombies or Peggle, but Fallout 3 type games might stutter or suffer severe performance issues.
You don't really need to know or care about what's the difference between Intel or AMD if all you're going to use it for is general computing needs. Just know bigger numbers = better performance. A $100 increase for a gig of ram extra isn't really worth it, IMO. You won't really need more than 2 gigs of ram. Look at battery life, sturdiness, customer support. Really, the biggest thing to look at is to make sure the reviews are positive and whichever laptop you're looking at suffers few problems (every laptop will have its problems, just find one that has the least). If you are looking for something cheap, just get something cheap. Especially if all you'll be doing is "school work, internet, storing photos, watching videos, and storing music." The extra dollars you put in isn't going to be worth it unless you go all out.
E-machines are quite easily the worst brand of computers to buy. Stay away... but lesson learned, I suppose.
Best brands to look at are probably IBM, Dell, HP... I don't know too many people with positive Compaq experience.