Would suggest a SAC305 alloy wire and unless the soldering job is particularly troublesome, use around a 1% flux core which is rosin-free and halide-free. You may wish to find a flux which is similar chemistry to existing lead-free paste and wave solder flux too. 

All the usual suspects (Alpha, Henkel/Multicore, Indium, Kester, Qualitek etc etc) will have suitable products. Suggest you ask for sample (small reel) from various suppliers you are comfortable with based upon your preferred criteria and let them choose what they find works best for them. Having done this before, ours picked Alpha FT2002 - but the deciding aspect at the time was the green colour of the plastic spool which easily differentiated it from the reels of SnPb solder on the benches!