If you want to stick with Serato then yes you’ll need to pay for the expansion. You might want to check out Mixvibes Cross DVS. 129 USD/Euro for software with two vinyls. It will work with your SX2 but will support any suitable sound card. This version also supports full HID support on all Pioneer CDJs and video mixing/sampling.
I’d like to point out that while buying DVS isn’t all that cheap to begin with, upkeep is most definitely an issue. If you are going to be active in playing/practicing, you’ll be looking at approx. 100 bucks a month in upkeep (needles and vinyls).
As for getting the 1625s to work, get a can of compressed air, blow out all dust, check if all pivotal points are running smooth. Check if all buttons and the fader are working correctly. Slap on two Ortofon stylii (shell & cartridge integrated). Dial in the weight and you are good to go.
Oh, and some fresh slipmats if only for cosmetic value 🙂