I'm with O2 broadband & they come recommended. Related threads at PCA - click here, click here, click here & click here.
You'll only need a wireless adaptor, if you cannot connect your PC direct to the supplied O2 wireless modem (they call it a 'wireless box') - e.g. if your main BT phonebox is too far away from your PC, or you don't have a phone extension cable close to your PC.
You'll also need one if you have an additional PC/laptop that does NOT have inbuilt wireless, but needs to be connected to your O2 Internet connection wirelessly.
If you do need a wireless adaptor....I'm using this click here (£10 delivered). It works fine with my O2 & XP Pro. You may be able to get one cheaper on eBay, & also consider a PCI wireless card (got one for £5-6 off eBay a few months ago). G