The first link is actually a wood burning kit. Probably can solder with it, too. I think I'd get a kit made for electrical device soldering.
I don't recommend the gun type for a beginner. It adds another level of learning the process regarding how long to hold the trigger to get the proper heat range. Its kind of like using sledge hammer to tap in small staples or brads.
You'll have enough to deal with using a constant temp tip, and learning to hold it on a metal mass just until the solder begins flowing. You just don't need more heat than what is needed to make the solder flow, and not so much that the flux burns up. For soldering the connections in this project, 25-35 Watts will do the job and allow you some time to observe when the solder melts, indicating you have the ideal heat. A gun will heat up so fast that you will get way past melting temp in a hurry, and if you don't modulate the trigger effectively, the heat will build to make the insulation melt rapidly.
If you spring for a tip regulated temp iron/pencil, it will make your learning curve a bit easier, imo. Solder (60/40) melt at around 370 F. If your tip will hold 400- 450 degrees, it will try to hold that temp for the metal mass you are heating. Then it is a matter of having enough power for the mass being heated. Large heat sinks will require high power. But, since the items you are heating are pretty small, 25-35 watts is all that is needed, even for temp controlled irons.
I still have a gun I got while in high school in the sixties. I haven't used it since the seventies, when I started working on circuit boards. It was pretty hard not to damage the circuit board when using the gun, due to excessive heat, not to mention wire insulation. Of course, if you still have asbestos based wire insulation, like we had in the 60s, the gun will be fine.