Obviously a good set of tools is essential. I have acquired various electrical, electronic and mechanical tools over the years. Buy the best quality tools that you can afford and look after them.
Various small cutters & pliers, desoldering & cleaning, IC & trimming tools
Desoldering Technique especially for IC's.
Somtimes I'm lucky, just carefully heating each pad using a soldering iron with a small bit and a solder sucker will release the IC, maybe with a bit of help from an IC extractor tool. This often works with single and double-sided pcb's. With multi-layer boards and with pads having a large copper/track area to dissipate the heat, more heat is needed with a larger bit. Great care is needed not to lift the pads. In some difficult cases I apply more solder to all the pads then try to heat them all at once to extract the IC. You can buy soldering iron bits for this purpose with 14, 16, 18, etc, points but they are expensive.
After removal, cleaning up each hole and track under a microscope makes fitting the IC Socket easier and avoids short-circuits between adjacent holes and tracks. Run a small piece of solid wire through each hole to make sure there is no obstuction. I also continuity test each pad to all its destinations on the pcb, plus appropriate low voltage insulation tests between holes and tracks both before and after fitting IC Sockets. At least you know that the pcb and the circuit diagram are correct. This can all take a lot of time, typically an hour per IC. Patience!
I also have a desoldering tool which has a hole through the centre of the bit connected to a solder sucker. Very useful in some situations.
As well as a small magnifying glass and bench magnifying lamp, I have a Prior Microscope. This has x10 and x20 lenses and a lamp for illumination. Essential for examining and repairing pcb's and small parts, especially as my eyesight isn't as good now as it was when I started my electronics career.
I also have some magnifying glasses (spectacles) to wear which sometimes help when soldering, etc. My wife says I look like a real geek with these on, but hey it helps to focus!