The 360 is wireless already.
The item you need first is actually wireless modem router (both names together). That would cost you about £30. Netgear products are a good place to start.
http://www.netgear.co.uk/wireless_adslrouter_dg834g.php
To play online you'd need an X-Box Live account. For which there are two options, silver which is free, or gold which I believe is £40 or £50 a year.
http://www.xbox.com/en-US/live/memberships/?WT.svl=nav
Of course one assumes that you already have an ISP at home, but if you dont try looking here for comparisons.
http://www.broadband-help.com/providers/list/advanced