Wireless broadband packages just mean that they give you a wireless router in the package too. But these can be bought separately, so if you can do it cheaper then do.
Pretty much any speed should be more than suitable for you. An average 2Mb connection will be fine. If you have a cable service (NTL or telewest basically) in your area, I'd recommend that over ADSL broadband. That's only based on my experience though.
Crucially, check the download limit on various offers. Many are "capped," so for example you can only download 2GB of data each month. After that they'll charge you �x per extra Gb or some scheme like that. Since you want to download music, if you download a fair bit you'll want an unlimited service.