Solder pumps are all sort of disposable, they wear down fast with the solder dust/bits inside them.
I recommend cleaning them after use, at my workplace I only have Ersa tools(probably over 200k € in soldering, IR, hot-air, heat beds, irons and a BGA rework station in my room), and well, I have a couple Ersa solder suckers/pumps, they cost about 20€, yes, they are a bit better than the 3€ ones, but not by much.
After 2-3 days of use I must disassemble it, clean all the solder, scrape the solder from the spring, remove the oring, clean it, lube it a bit(I use flux paste, have lots around and does its job), and every other week I need to stretch the spring.
The tip only melts with the iron set to 400ºC and when doing something like that damage to pcb is very likely to happen.
Almost all the solder wicks need flux, even brand names, the flux stays in them for so long that it dries, aplying just a bit of flux to the joint before puting the wick over the joint does wonders, when fighting with big 6-8 layers pcb's full of power planes, lots of flux, wick on top, then add a bit of solder, it increases the thermal conductivity of the iron a LOT.
For starters/newbies/not so rich people(like me), go for a 30Watts iron, the Hakko clones can be good, IF you spend 10€ to buy an original Hakko tip, a chisel tip wit 2-2.5mm wide is perfect for PTH and to solder almost all the SMD's out there, from 1206 to 0603, TQFP's,SOP's,SOIC's, even the QFN's with exposed pads are easy to do, when they have power planes and you did design the pcb, leave a 1.2 to 2mm via under it, then just apply flux, and feed solder, it will solder the power pad fine going that way and you wont even need hot air!
There are lots of tips and little tricks to solder the strangest components, just remenber, flux is your friend, from Mouser(and Digikey I assume), you can buy a 200-250MmL seringe of Flux from Multicore or some other name brand, go for organic no clean flux, they are less acidic so if a bit stays behind some component leg it doesn't kill the pcb, will just be a nice dust trap and it also doesn't eat your iron tip.