I'm looking at the Nokia HS-12W for the same purpose (music + handsfree). An alternative could be the SE HBH-970 (or something like that, also a stereo headset with lcd), but I prefer the Nokia as I already have chargers to match and like the radio option. The SE does allow listing to audio from one bluetooth music device, while still allowing for handsfree operation (the Nokia requires both the music and the telephone to be the same device).
There is a software by jetwaremobile that should allow one to even see the caller name on the lcd display of the headset.
For the BT widget, I think you are looking for something like the Nokia AD-42w. It has both line inputs and line outputs, and can stream music to/from a bluetooth device. IIRC, Motorola also has something similar to the Nokia AD-42w, but I'm not sure.
(I'm thinking of getting this as well, to be able to use the Nokia HS-12w as a pair of regular wireless headphones - but I'm not sure about the quality).
There also is the HTC-S100 (bluetooth stereo headset, no lcd display), which you could use. It has a standard 3.5mm jack, so it should be no problem connecting this even to a line input of a hifi system.
I haven't tested any of the above equipment, so I cannot comment on the quality, nor on the compatibility of the hardware.