In my experience, a soldering gun is typically a higher wattage device which is useful for soldering wire-to-wire or large, clunky components where you need a fairly large heat reservoir. The soldering gun I have is Radio Shack 100 watt, and is excellent for when I need to solder some 14 AWG stranded wire to something, or even just tinning the end of it. (It's been replaced by a 150/230 watt version.)

For any through-hole or surface mount work, you definitely want a temperature-controlled soldering station. David Jones, on his EEVBlog, recommends the Hakko FX-888 for starters (and has a soldering tutorial showing it), though there are many other brands he recommends in a video blog about setting up your shop.

I used to use a 15/30 watt selectable Radio Shack soldering iron, and I was able to get a lot done with it for over a decade. However, once I got a Hakko FX-951 temperature-controlled soldering station, I can't believe I ever made do with the old RS iron.

Honestly if I knew then what I know now (a common phrase in EE, I find), I'd have picked up a $85 Hakko FX-888. Don't let the unusual blue-and-yellow case fool you; it's a solid unit. (Hakko indicates that a digital version of the FX-888 is coming in January 2013, so you might want to wait for that.)

You can also go with a Pace, Weller, JBC, Xytronic, Ersa... There's a lot to choose from. Temperature control will get you more consistent results, but as others indicate, is not as important on through-hole work.

One last point: The temp controlled stations tend to have a lighter, skinnier iron handle than the ones that plug into the wall directly. This to me is a major advantage in being able to work around and between components and have more control over a lightweight iron.