Your models 66 and 67 fit right into IDPA/SSR with speedloaders and .38 ammo that makes at least 105 power factor. You could use these all the way to the nationals. Need a strong-side holster, 4 speedloaders, and holders for 3 on your belt.
In USPSA, clip fed revolvers with major power rule revolvers(model 625), but you could use the K frames at club matches with a disadvantage.
My choice of your guns for USPSA would be the XD45 in Limited10, major power. Need 5 magazines and holders for 4, plus strong side holster that covers the trigger.
As to difference between IDPA and USPSA, IDPA is more designed to emulate defensive shooting, with concelament, cover, and stages limited to 18 rounds. Suitable for most standard carry guns.
USPSA is higher round count, more of an equipment race, and more complicated scoring rules.
I shoot revolver and stock service pistol in IDPA, and mostly Production and Limited 10 in USPSA......my favorite is PPC.