A Chinese "936" temperature-controlled soldering station for £15-£20 is better than an ordinary (uncontrolled) iron at any price, though you may well have to replace the original mains lead if they are still as bad as a couple of years ago. The bits are very cheap, but OK.
The other part is desoldering.
I like these:
https://uk.rs-online.com/web/p/desol...pumps/4794197/ (£22)
I prefer the CPC stations
https://cpc.farnell.com/duratool/d00...lug/dp/SD01384, but they are now £87.
I caused more damage to PCBs with poor desoldering tools and technique than with poor irons, but not for the last 30 years.
Whatever you get, I suggest practice on some scrap boards.
Martin.