Since you ask about soldering iron recommendations, I'm assuming you don't have much experience soldering electronics; maybe none.
This kit is on the easy side for soldering. If you don't have any soldering experience at all, though, I suggest you look around for a kit specifically aimed at "learn to solder". There are a lot of those around. They usually include some kind of forgiving circuit that is interesting enough to hold your interest but very easy to build. It's much better to make your mistakes on a $2-3 practice kit. Here is just one of a million examples: https://www.tindie.com/products/MakersBox/easy-joule-thief-soldering-kit/
(I have no affiliation with it).
As @squix78 says, what kind of iron you get depends on how much you want to invest. If you think this is the beginning of a hobby you will do for a while, then you probably want a pretty good iron. Since you don't know much about it, you'll soon be reading opinions about the ideal soldering temperature for various things. There are many temperature controlled irons around that don't tell you what the temperature is ... the just have a dial with no scale. You'll have no idea (pro tip: don't test it with your tongue!). So I suggest you get a temperature controlled iron with a digital readout so you'll know what's going on. But, again, only if the money makes sense to you because that will probably cost you $50-100 or more.
Finally, I recommend watching the youtube series on "Basic Soldering" by PACE Worldwide. https://www.youtube.com/watch?v=vIT4ra6Mo0s
Although it's aimed at those beginning a career in professional electronics assembly and repair, it's really informative for just about anybody starting out.