Personally I'm very partial to the Precision. I play a stuck-together p-bass made from parts (including the neck from my old Peavey bass and a Duncan-Designed pickup) and for both live and recording it's terrific. Incidentally, as a bass player I'm more the thuddy-melodic, old-skool Jamerson/Porter/McCartney style than this more modern hyperslaptive bass stuff.
The Rick is very nice, but to me feels and sounds less like a bass than a very large guitar that plays lower in pitch. A Precision can get much of that punchy tone just by cranking the tone all the way up and using light gauge roundwound strings. I've never tried it, but if you have one of those P-basses that have an extra Jazz bass pickup at the bridge I imagine you'd get even closer. I think the bridge pickup makes a crucial difference if you want punchy bright bass tone. Which begs the question: why not just get a Jazz Bass? I offer Geddy Lee as an example: primarily a Rick player but also achieved that tone with his Jazz Bass. And of course Jazz Basses are dime a dozen, especially when you count in copies.
As for Stingray type basses, I once played an OLP (Music Man's budget line) Stingray at a GC, and except for the lack of active electronics it seemed like a very nice instrument, great feel and a pretty good approximation of that Stingray funk bass tone, And best of all...cheap!
cheers
Billy S.