Those are three really good choices. I sing and play in a power trio and originally when I wrote the songs and started this band I thought the P bass would be my go to since I love Nomeansno and wanted a similar tone but play fingerstyle. Once the band got going, the Jazz bass ended as my main bass. It just fit so well. The music is a mixture of punk, prog, funk, metal and jazz. It's kinda like Primus, Nomeansno, Mike Watt stuff and Mike Patton stuff too.
I've been curious about a Stingray. I'm thinking about picking up one of the Sterling by MM models to see how it works.
Also with the Jazz, you have 3 really good pickup tones. I usually keep mine full on but there are songs where I use the front for a P like tone and rear for that Jaco type tone.