Do you need a special soldering iron?

Biggest danger to circuit boards is too much heat. You want an iron 20-30 watts with a small tip. Be sure it's well tinned and you're using rosin core (not acid core) solder. 60/40 lead tin mix is what you want.

Second biggest danger is making cold solder joints. If you're not experienced, practice on some scrap wire. Don't use too much solder - you can easily created unintended bridges between adjacent circuit board traces.

You'll want the solder sucker to help remove the old parts - beware of applying too much heat to the board during this process or you may cause the foil to lift from the board.

I don't think you'll need the glue gun.

Be sure to observe polarity markings (if any) on capacitors. Not all have them, but installing an electrolytic cap backwards will get you some nice fireworks.

Vman, thanks for the update. You're right about the iron wattage - lower is better. Actually my tool of choice is a temperature controlled iron. These use a sensor at the iron tip and deliver just enough power to keep it at the right temperature. You can also dial in your desired tip temperature to suit the solder and job. Absolutely the safest iron for PCB work.

I paid about $80 for mine 10 years ago.

I still like the solder sucker better than the wick.