The cabinet does not look too bad. I would give it a clean (I use Krud Kutter) & then ponder whether you really wish to do a full repaint.
As far as operations are concerned be very careful that you do not tackle more than one concern at a time-so easy otherwise to cause additional problems. Based on what you have said concentrate on the slingshots and pops initially. There is a plethora of info available in pinrepair and pinwiki sites to help you on these two areas. Start small and when you gather confidence go bigger.
Overall you got a great deal.