Rewiring project - what type of wire to get?

My epiphone Dot's innards died (pretty much one by one) and now it's getting all new pots & pickups. I plan to use as much of the existing wiring as I can get away with, but I'm gonna tap the coils and that means adding stuff. Looks like the existing wire is light guage stranded, I don't know much about it though.

So when the components get here in the mail I will head down to Radio Shack and ask for _________?

And as was suggested on another thread I will definitely need to do some practice solders first.