Although I generally avoid soldering to pots (I don't as a general rule do guitar electrics repairs if I can avoid it) I've found some pots don't take solder very well and may need abrading. From other posts on this forum this seems a common finding.
Trying to get a decent solder joint with a cheap, under powered soldering iron is hard work.
Unfortunately the maxim "buy cheap, but twice" is very true for most tools; however if you don't do much soldering it's very hard to justify the expense.
If you do any appreciable amount of soldering you will now encounter a variety of different solders, and so if you can afford it I would recommend getting a 50W temperature controlled iron.
We use 50 W Weller Magnastats. These have the advantage of a very simple temperature regulation mechanism (different tips give different temperatures), and you can get a full range of spares. They are quite expensive though (over £100 new), although you can save a bit of money if you want to build your own 24V power supply.
A bit cheaper option would be a Weller W61 60W mains temperature controlled iron. The advantage of using a 24V supply is that the element lasts longer and current leakage is lower, but if you aren't doing that much soldering then a mains iron will be fine.
I don't have any experience of Antex or Xytronics irons, although there seem to be plenty of people who recommend them.
As another "top tip", with the advent of higher melting temperature RoHS compliant solder, I was recommended to use low abrasive brass wool for tip cleaning rather than the wet sponge. This has the advantage of not lowering tip temperature which can cause the tip to crack and reduces tip life.
Regarding the solder Feline mentioned, this is 62% Tin, 36% Lead, 2% Ag. It costs about £14 for a 250 g roll from Rapid (see link below). It has the advantage of a low melting point and a very narrow temperature of phase transition, so your chances of a dry joint are very much reduced. I use this for all our repair work.
This solder is not RoHS compliant, so obviously I would not recommend it is use in new equipment......
http://www.rapidonline.com/Tools-Fasteners-Production-Equipment/Soldering-Equipment/Solder-Fluxes/Future-HF-low-melting-point-halide-free-no-clean-cored-solder/60030