I think my only solder sucker was a red Radio Shack rubber bulb with the teflon tip. Probably cost me about 2 bucks about 40 years ago. I used to build slot car chassis from brass and piano wire, so it got used a lot to clean up things. Last time I tried to use it, it was dry rotted and cracked... went into the trash.
A real rework station with heater, vacuum and iron with temp controls is the kit. My little brother has several of them but he does industrial electronics repairs. I have a modest rework station that I bought last year and just got out of the box as I just finished a work area upstairs for doing instrument and electronics repairs and setups.