I say go for it! Mass Effect is an AMAZING series (one of my favorites) so I'm always one to recommend it to others.
You don't need to pay for Xbox Live if you don't play online (which is mostly just for shooters anyways on 360, mostly), you can still download with a silver account which is free.
Wired hook-up is always better (especially with the nasty things I've been hearing lately about Wi-Fi and cancer, ick) but the older model of Wi-Fi g model (I think it's a g?) should be pretty cheap if you can find it. But if you're looking into games like Alan Wake and Mass Effect, you may not need to hook up anyways.












