I think you can use wireless adapters made by random company's. When i was looking on Amazon a while back alot of the comments mentioned if it was suitable for xbox live or not as far as i can remember. I ended up buying the official adapter for about £60 though for some reason, probably because im an idiot and could afford it at the time. As for the gold package, i think my one year membership card cost about £35, which is well worth it considering how much online gaming adds to the experience.
If you want the cheapest way look for wireless adapters on amazon or something, but the membership card should cost £35 regardless.
I remember i got xbox live for the exact same reason, beating strangers at pro evo.