I could be wrong but, to my understanding any wire will work.
The way wire and electricity works is like this:
The gauge is the thickness.
The Thicker the wire, the more energy can pass through it.
Non-Insulated Wire can be a fire hazard/will impair your circuit/connection.
Think of energy as a giant elephant. Now, think of wire as....say... a road (or better yet, a loop/ring.) The elephant is 10 feet wide, but you chose a 5 foot wide road (or ring) for the Elephant to walk on (or through). The elephant is going to step outside of the road and mess up the pretty grass on the side of the road(or break the loop/ring).
Basically, if you have too much energy running through a wire, it will burn out and break (which caused by the wire heating up from, well, too much energy through it) -which is how a Fuse works. A thin wire (but not too thin) designed to burn out and break the connection if the energy spikes for some random reason. -Redundant, I know but it helps get the point across.
Use any wire you want so long as you can attach it to the other parts of your project.
Using Solder is preferably the best way to make the connection. If you are unable to use Solder, use small bits of Aluminum Foil, wrap it around both wires TIGHTLY (Pliers work fantastically) and then hot glue them together. While the glue cools, pinch it with your fingers (or some other tool) to get a nice, tight hold AND connection.
Choosing wire gauge: I do not know the specifics but work WITH the wire size you have on the EL wire. You dont want to have a big fat 40 gauge wire hooked up to a 3 gauge. The HIGHER the Gauge, the thicker and less pliable (movable) it is. Yes it can take more energy however, it will take more power to get from point A to point B.
I believe I use a 10 or 15 gauge for all of my electronics. You can find some at your local hardware store / Walmart
Hope this helps.