A 12" Mac iBook G3 with wireless running an old version of iTunes. Is plenty fast enough and looks pretty enough. Will have to keep it plugged into it's charger as unlikely to have a very good battery. Will be more user friendly and arguably better sound quality than a cheap plastic, unknown brand £100 DAB/internet radio thing from the shops.Find a friend who wants rid of one or pick one up for £10 or less e.g.
http://www.ebay.co.uk/itm/apple-ibook-g3-dual-usb-with-cd-rom-/281178271969
P.S. iTunes does internet radio if you wonder why I mention it. You would also be able to still find internet radio software that runs on old versions of OSX to install for free, FStream or similar.