I've been playing fretless in everything from punk to jazz for decades. As long as your intonation is good and your tone and lines fit the song No Problem!
My Yamaha APX-B12F. I use it for everything. I've used it in a country rock band, a soul band, a folk band and a jazz band. I haven't picked up either of my solid bodies in at least 5 years.
I have a Yamaha APX-B12F, didn't use it for years until the right band came along and I found the right strings. The band was country rock and the strings are Labella low tension flats. Since then I've been using that bass in every situation I play in regardless of genre.
However it is only...
I started out on a Fretless P, moved to a Fretless J and then to a fretless PJ with a P body and J neck. Now however I play a fretless Yamaha APX-B12F as totally different Beas. But to your question I'd go with a PJ, to me the most versatile.