I was in a similar position to you a few months ago and now shoot pistol targets most days. Where do we start, well compact is a good start as it has a proper grip that makes you take a proper drop wrist hold - within budget new, HW45 is a springer and has some recoil - some love them some do not. HW 40 & 75 ssp nice triggers 40 within budget, FAS 604 good SSP within budget secondhand. My favorite would be a FWB 65 recoiless springer - this was used in world champs up till late 80's within budget s/h I love mine.
Get your eye in and join us in the MPL league postal comp. for the next season starting in a few months time MPL = muscle power league all powered by muscels not co2 or compressed gas.

Hope this starts you thinking

George