INTP: Generic rebranded soldering iron. It will work just fine. The tips it comes with will probably literally only last a job or two as they disintegrate, but it takes Hakko tips which work great.
I would buy a proper stand for the iron, a brass wool in a can for tip cleaning, and 63/37 solder.
Rosin core means it has flux in the middle of the wire, which is fine for just about everything you'll do. Unless you plan on working on some grody oxidized components from decades ago, it should be all the flux you need in there.
And you're right that it comes with 60/40 solder, but it is definitely not going to be kester. Whatever it comes with will be usable, but you should look for good solder (such as kester 63/37) as that makes the most difference in your results.
Which tips specifically should I be getting? I don't really want to spend more than the $20 for the iron and $14 for the third hand/stand/magnifier unless the tips that come with the iron will really disintegrate.