I bought the Make: Getting Started with Soldering Kit at the Bay Area Maker Faire earlier this year. I recently completed the set of blinky badges included.
The one on the far left is from months ago. I’ve improved a lot since then, as seen by the rest of the badges.
It’s a good start, but incomplete. You will also need:
Goggles. The web page for the kit explicitly acknowledges this. You need eye protection because a blob of solder can go flying when you’re cleaning your iron. This happened to me—fortunately it didn’t go in my eye, but I made damn sure right then to get out my safety glasses and wear them for all further soldering.
I had the freebie Google-branded safety glasses that they hand out at Maker Faires, but if you don’t have any, get some.
A soldering iron that isn’t trash. The iron included in the kit takes forever to heat up, and it’s oxidising all the while. Don’t waste time and energy on it—spend the extra $50 or so to get a good iron.
Mine is a Weller WES51; it heats to operating temperature in under a minute, and has an LED to indicate when it’s ready.
A desoldering iron. I found trying to desolder my mistakes using the included solder-sucker tricky. It might have gone better with the better soldering iron, but I already had this thing from Radio Shack by then. It’s not ideal, particularly in how long it takes to heat up, but it’s still better than an unheated desoldering pump.
Note that you need to tin the tip of a desoldering iron just the same as a soldering iron. In this case, the “tip” is the flat, ring-shaped surface directly around the hole. Lay some solder across the hole, then suck in any excess and spit it out onto your sponge.
Tip cleaning wire. I use this Hakko model. The wad of metal is an abrasive cleaner that you’ll need any time you get too much build-up on the tip and the wet sponge isn’t enough. Ideally that should be rare, but if you find yourself unable to tin your tip because the solder won’t melt or won’t adhere (“dewetting”) and the wet sponge doesn’t help, you probably need to jam your tip around in one of these for a bit.
Educational resources. The Make kit comes with a little booklet that isn’t bad, but I needed other sources of info: