I agree with just about everything said about soldering above. I use "plumbing solder" (Oatey Brand, from Home Depot. This, along with a large bottle of Stay-Brite soldering flux (8 ounces = lifetime supply) will be fine.

A larger soldering gun will make quicker work of the soldering task, but a smaller iron will do fine too. Just make sure you heat the work, not the solder. Don't just drip molten solder on the joint and expect it to hold. The metal parts have to get hot enough to wick the solder into the joint. When it does, it's amazing how little solder is really necessary to get a strong and tight joint.

The big thing here are the "3 rules of soldering"

1- It has to be clean

2- It has to be clean
and
3- You guessed it, It has to be clean!

Don't solder the threaded end of the wire. The solder clevis at one end will be solidly installed. The adjustable clevis at the other end needs to stay adjustable. Just install a jam nut on the threads, snug it up against the clevis and you will still have adjustability for later in the plane's lifetime.