Hmm, let's see.
Well, if you want to play games online, then I would suggest having a good internet connection and a fairly decent operating system. I would suggest something with a pretty good graphics card.
If I were you, I would go to your local Best Buy or Future Shop or whatever you have where you live. Tell them that you want a decent computer, one that can play games without too much lag, and a decent price. Pretty much all the stores will probably be having a back-to-school sale, so now's your chance to snap up a lappy for a decent price as well.
My laptop is a HP Compaq, and it was $499CDN. It has exceptional graphics, and it's a pretty decent computer overall. I don't have too many problems with PC gaming, though anyone will tell you that if you're a hardcore PC gamer, you should probably go with a desktop, rather than a laptop. I don't play a whole lot of games on my laptop, but it might overheat a bit.
So, yeah. I hope that helps you out a bit.