Lots of recommendations for mini-systems but if you like your current amp and speakers surely you just need a DAB tuner
Hifi separate DAB tuners seem to be remarkably expensive (and the one cheap one gets lousy reviews). If you don't mind the odd size there are TEAC T-H300DAB 's on eBay both new and used that look OK.
30pin ipod connector to Phono leads gives a line level output which should sound better than the headphone socket. Doesn't work on the 5 - you need a dock or expensive cable for that as no line out over the new connector.
Bluetooth or Airplay from the phone for convenience for music. Lots of options. I *think* Airplay is better quality as BT is more compressed but someone else will confirm
Having used streaming radio on Squeezeboxes, and tried using a TV set top box, nothing beats the 'just works' convenience of a DAB tuner - I'm in the process of collecting things for the new house.
A Yamaha RX-V500D Dab receiver (<£300) will go in one room. DAB, Airplay streaming, Internet radio/DLNA. Seems to do everything but very plastic-y construction
Teac CRH260i DAB (£180 at Richer Sounds) for another - DAB, BT streaming and has both Line-in AND line-out (which is rare on mini systems with DAB).