The soldering iron advice I wrote below it should be helpful though
The sad thing is that the more expensive irons are a lot easier to use. I think (in the uk) the most important thing for someone doing it for the first time is to use leaded solder with an easily cleanable flux core. Make sure not to use plumber’s solder and flux! I’ve genuinely seen some smt eurorack modules I’ve repaired that were soldered with it!
For an iron it’s almost a case of just pick a price you want to spend - £10 - £25 any old antex/amazon etc non-temp controlled iron; £100 ish get a hakko: £150+ weller wtcp, £200+ ERSA, plus a few other brands…
If you do go down the kit route (or even if you buy the iron etc individually) I’d highly recommend getting a desoldering pump too. You could use desoldering braid but I find that works best on flat surfaces like PCB’s. Essentially the pump creates a vacuum so when you heat the solder and it starts to flow you can ‘suck up’ the molten solder. Essential for de soldering and you’ll prob want to do a bit of that when starting out! The only caveat with them is when you release the button there is a jolt as the internal spring decompresses…this can be enough to dislodge delicate items but for plugs etc you should be fine. Some folks won’t entertain using them and insist on braid but it’s horses for courses… I’ve used both for years without incident. (Apart from once sucking a pad straight off a VERY old PCB that was basically toast anyway!)
This is ideal for the task. They’re only cheap so you’ll prob find them included in soldering kits like the one posted above.