I would suggest you invest in a 360 and Halo 3. I would normally say its the best for online gaming, however, assuming your are young, that might be an issue for your parents (as is the cost of playing xbox live [dumbest, yet most successful idea ever]). The advantage with the 360 is most xbox games are coming to their version of “Virtual Console” so, I know that Halo 2 is due out sometime next year. Plus the plethra of games already out for the 360.
In summery, If your mom is willing to front the cost of the 360, I would go with that, with a note to say if you can buy new, DO THAT! buying used is a risk with the 360 (the red ring of death).
I assume you are probably like most kids (10–18) who don’t care about the story, you just want to shoot other people in the head and call them names, along with some form of strange speech that requires you to shut off half your brain to understand, so I would get Halo 1 cause that is fun to play with friends in co-op, skip Halo 2 cause it was glitchy, and far to unbalanced, then get Halo 3, play on co-op with friends, then head online (if you can afford it) and play some co-op on line, or some “death matches.”
One other advantage is xbox arcade. I swear by that system. You can buy games online and keep them on your console, they are cheap, and really addictive. Not to mention I find more of my friends play those then actual store bought games. And if your mom had reservations about using her debt card online, you can buy point cards at any store, including 7\11.