I've been turned off to cheap soldering iron kits, I've had a couple of them and they never are quite as precise or perform as well as a proper iron would.

If you're looking for something cheap but still a solid choice, this is what I use right now:

YIHUA 939D+ Digital Soldering Station, https://www.amazon.com/dp/B07RVMZNYR/ref=cm_sw_r_apan_glt_i_93TV5JM8J14MBSYQAVWK?_encoding=UTF8&psc=1

It's digital and comes with most of what you need to get started, and I've abused it quite a bit and it still works. I'd recommend grabbing some lead solder and a flux pen as well, it's easier to work with and makes a big difference!

But basically, a soldering station with a digital temperature control will do you better than the plug-right-into-the-wall sorts

That's a toughy. The WLC100 that was mentioned is okay for most stuff but I wouldn't recommend them for fine work such as this simply because the pencil is too thick and uncomfortable after a while. But it is a Weller and the temp controls are very stable and accurate.

Aside from that, way before I upgraded to this I did use this which isn't too far from 50. It covers all the bases and uses hakko clone tips (irc) which are easily replaceable. If I were to recommend anything else it would be this because of the iron and tips. I've used similar irons and had no major issues with them. Hope it helps :)