Hi.
I'm partial to my Weller WECP20, but basically anything from ~25W will do nicely if You use ground lugs.
If You want to solder the grounds onto the backs of the potentiometers, you'll need something a lot sturdier IME.
De-sodering wick and good quality rosin core solder are very handy even though the good old wet rag and an old toothbrush will work in removing the molten solder as well

.
As for the solder, the leaded varieties are quickly vanishing and some of the lead-free ones are PITA to use. Especially with the lower wattage irons.
Even though the price tag is scary to say the least, the
Mumdorf M-solder Supreme I use is actually easier to use than some old leaded ones.
You'll also need something to wipe the tip onto/with, KEEP IT CLEAN is the first rule in soldering.
Wire cutters and wire strippers come in handy when You grow tired in using your teeth and pocket knife to do those tasks.
Regards
Sam