This is the best solder I have ever used. RadioShack SnPbAg 62/36/2 Silver-Bearing Rosin-Core Solder, 0.015" Dia?
Radio shack has a few stores still open but they have turned mostly to internet sales. That solder is thin for small work and is silver bearing for a higher conductivity with a low eutectic temp.
Since the “Recommend soldering iron” question pops up quite often, I’ll point you to this recent thread for a soldering iron.
soldering iron recommendation for simple work