Yes, 60" shaft is what you want - but you can re-shaft a 54 or even 48 with a 60 shaft and wiring - not a big deal. Obviously, starting with a 60" would be easier - but you are right - 60" usually only is available in 24 and 36 volt motors. The manufacturers recognize that a 60" shaft is likely going on a bigger boat and most of those folks are going to need more than a 12 volt motor.
Regarding 12 vs. 24 volts - do you have 2 batteries on the boat now? A 12 volt trolling motor may not be enough for a 20 foot boat, and remember a 12 volt TM running on a single battery draws twice the amps compared to a 24 V pulling the same thrust. If you already have 2 batts, it's easy to put them in series to power a 24 volt motor - the starting battery remains connected for 12 volts, and the other (should be deep cycle) is connected to the starting battery in series to get 24 V for the TM. That's what I have done on my CCP and I run the TM a lot when fishing. My 24 volt MinnKota struggles on a windy day, but it is adequate to move the boat 90% of the time. Regardless of the TM, it's just a PITA to fish when it's really windy.
Remember you will need a 50 amp breaker and at #6 wire to run to the bow to power your TM. I also recommend a quick disconnect mount so you can remove the TM if you want without tools and leaving ugly holes in the deck. Both MinnKota and MotorGuide offer quick-release mounts. If you are looking around for a used motor on eBay or Craigs - look for one with a quick release mount and you might save some $$$.
Hope this helps - good luck!