I always reccomend this kit for beginners. It’s cheap, decent quality (lasted me over a year as my first iron & multimeter), and comes with everything you need to get started except for some SPDT mini toggle switches and an assorted potentiometer kit.

Its best to keep it simple & cheap when you’re starting out imo. With these 3 purchases you should be able to get started right away for around $40. The kit def isn’t BIFL, but its good enough to keep you bending for months, & gives you time to figure out if this is a hobby you want to keep going with & invest in down the line

A task like this isn't very difficult, you should use the small tip on the potential soldering iron you might get.

You should put the solder wick on the pins and then press the soldering iron on it, not for too long though. Just enough for the solder to melt and get absorbed by the solder wick.

Also don't forget the flux for better flow. And yes those kits on Amazon could work. I would recommend this one since it has a lot of stuff for around 30 bucks and some nice reviews.

Happy soldering!