I use rosin core solder that I pick up at electronics stores, acid core will cause rust and binding..
 As for what to use when soldering the wire I use a Weller 140-100 watt soldering gun that I picked up at Home Depot or Lowe.s.
  I have used Mapp gas when using silver solder, but for most soldering I just use the soldering gun.
  Of course the wire has to be clean, and I use sand paper to get it "shiney" clean.
  Also if splicing the wire, I clean both pieces and wrap with fine copper wire then solder...
 I hope that this answers your questions and if I can help again just say so.....
 

When soldering music wire, etc., do you guys use acid core or rosin core?
Silver solder and MAP gas? Or is that too much heat?

There is a very good silver solder called Stay-Brite. It is available in a number of Hardware stores and most good hobby shops. I do not know if such continues but a few years ago , Geat "Pains" sold it in their own package labeled "Silver Solder" GPMR8070.
Stay Brite is very strong. It can be easily done with a decent size soldering gun. Those 15-40 watt electric irons will not do well with landing gear etc. Fine for electric stuff, but not hardware.

A little trick, contrary to all the politically-correct methods of soldering,    is that I apply the liquid flux, sparingly, heat the job a bit, melt some stay-brite, then a few drops more flux and things began to run very well.
There is another good one, usually found in the RC Car departments called Dean's Racing Solder with about the same silver content of Stay-Brite. It works well, but I definitely prefer Stay Brite.

Tom,

Hmmm, mine's a fairly old one. Has big bolts. I bend the right angle in legs of the copper tip after putting the nuts on the legs, then just maneuver them into the holes in the side of the contacts then thread the nuts in. The clamp to the right angle bent legs of the copper tip pretty tightly.