After scouring blogs and forums, looking at recommendations from Rob Robinette's site, I came up with a list of tools for the project. Everything in the picture set me back around $250 ordering from Amazon...yikes.
Used Weller WES51 Soldering Iron
I did a lot of research for the iron because this was the most expensive tool. I figured going with a better iron would make learning to solder well less frustrating, which is worth a little extra money. It looks like the Weller WES51's are worth something if they're kept in good condition.
Used Proster V99 Multimeter
I saw so many people say that Fluke makes the best meters, but those were too expensive for me. I got one that is auto-ranging and that measures capacitance.
Hakko Tip Cleaner - This worked well and was glad I got it.
Tip tinner - Didn't use this.
Chisel tips - Only used the medium sized chisel tip and didn't need anything else.
Solder sucker - Worked great.
Solder wick - I felt the solder sucker was easier to use.
Flux pen instead of the paste - Didn't use this much, but probably should have.
Small needle nose pliers - Necessary.
Wire cutters - Necessary.
Heat sink clip (so that heat doesn't fry a component) - Didn't use this.
Alligator clips - Used a clip a few times to hold down a component when soldering.
Helping hands with magnifying glass - Very helpful.