when replacing components on used circuit boards I always cut the legs, also I always add some fresh solder with my soldering iron to the pads before I desolder (helps with the heat transfer)
I always use a good quality solder with a good quality flux (poor quality flux will corrode the pads and tracks on the board if its not removed and will shorten the life of your solder and desoldering tips)
I only use thin solder when soldering components (0.8 mm)