Soldering is excellent for e.g., plumbing and printed circuit boards. For wiring, crimp connectors with a quality crimper are superior to soldering. A soldered joint is not flexible like a crimped joint is, and if forced to flex (or through vibration over a long period of time), the solder can crack.
With that said, if you do want to solder wires, unless you are trying to solder some heavy gauge wiring or terminals, then a soldering iron is what you want. A typical soldering iron should be fine for soldering up to say 12 AWG wires.
The best name in soldering irons in my opinion is Metcal, but those can run you $500 or more. I used one working in a PCB factory for 2 1/2 years, soldering about 1000 boards a night, and nothing else compares, no matter how much you pay (I have one of my own now that I got a good deal on used). However, soldering wires is neither delicate nor precise work, nor does it require the 10-seconds-to-reach operating-temperature or lightning fast recovery time of a Metcal (which is important for production line work), so a Weller would be fine, or even a cheap Radio Shack iron, or most anything for that matter. I've even soldered with a flat blade screwdriver heated with a propane torch before (works fine in a pinch).