Generally, if you can, get the leaded solder. It's generally not ROHs compliant but it makes a longer, more stable connection. Lead free solder's what's used in Laptop and computer motherboards and that's why so many of them breakdown if you over heat them--- some components get unsoldered. Though for the temperatures used for a turntable, it shouldn't matter.
As for wire, use any from 34 to 28 AWG tinned or untinned copper. You can get this from mouse wire, USB wire, or miniHDMI cable (34-30 AWG). The resistance per yard of those is actually less than than the resistance in 18 inches of Dual or Garrard tonearm wire according to my Radio Shack meter.