Although I've soldered many times before, but I never really thought about the details of it. A soldering iron is good enough if you just want to use for automotive purposes, you don't need a $300 Weller one, something $15 is good enough. For the solder, just get a thick/thin enough gauge so that the iron can melt it relatively easy. Be sure to heat the wires and apply solder onto the wires, not heat up solder and apply to wires. Use a wet sponge to clean up the tip in between soldering jobs. Once you're done, leave some solder on the tip for next time, this way, the tip will not get corroded.
The 15-watt should be capable, but if the heat isn't high enough, a 30-watt should be good. The gun-type has a higher starting temperature, but typically a 30-watt should be fine, as well as the resin core solder.