@SteveC, IMO and experience, you can make *just about* any P bass sound great with a pickup and string combo you like (I know there are huge differences in quality, but the P sound is unique in that it doesn't require as much tlc, imo, as other pickups). It would be a great way to scratch your itch for a P, not break the bank, and still be happy with the sound and playability.
For example, I rehabbed a garage sale no-name p-bass, refinished the back of the neck and gave it a setup, replaced the bridge, dropped in my favorite P pickup I had (a classic Bart), and installed TI Jazz flats. I'm not saying every cheap bass could turn out this good, but I probably have about about $200 into it at this point, and I have recorded/gigged/enjoyed it immensely. Being from the midwest, I also like explaining what a good deal I got on a very good-playing, great-sounding bass.
I also sanded the red off the headstock, refinished it and had a water slide decal made that says Superbad FUNK BASS. I thought I was clever at the time. This whole thing was also a fun project.

For example, I rehabbed a garage sale no-name p-bass, refinished the back of the neck and gave it a setup, replaced the bridge, dropped in my favorite P pickup I had (a classic Bart), and installed TI Jazz flats. I'm not saying every cheap bass could turn out this good, but I probably have about about $200 into it at this point, and I have recorded/gigged/enjoyed it immensely. Being from the midwest, I also like explaining what a good deal I got on a very good-playing, great-sounding bass.
I also sanded the red off the headstock, refinished it and had a water slide decal made that says Superbad FUNK BASS. I thought I was clever at the time. This whole thing was also a fun project.


