With your only stated tone preference being "very versatile" you're going to get a whole lot or recommendations from all of the folks here.
The sad fact is that most of those recommendations would tell you more about our tonal preferences than yours.
The trick with only using the word versatile to describe the tone is that there are tons of jazz style pickups that are honestly quite versatile. Person A could say "Bartolini 59J1s" and Person B could say "Seymour Duncan SJB-5s" and Person C sound say "Nordstrand NJ5s" and Person D could say "Delano JC 5 ALs" and
they'd probably all be right.
I think all of those pickups are, in reality, quite versatile. They don't all sound the same, but you could take any of them to a rock gig and do well, then a funk gig and do well, then a pop gig and do well, then a jazz gig and do well.... etc. etc. etc.
So much of the tone we produce is in how we play the instrument, any preamping or EQing we do to the instrument, the gain staging we employ and our amp setup that you can take many many pickups and cover a broad sonic territory with them.
Don't get me wrong... I do think that there are some pickups that are a lot less versatile than others. I do think, however, that the set of pickups that can reasonably called "versatile" is as big or bigger than the set of pickups that can be called "not versatile."
Conclusion
More info! What sort of sound is it that you're after? What sort of tone do you want to hear out of this bass with all EQ flat and just plain jane playing. What's the "home tone" you want out of your bass? What particular sonic directions are you wanting to go?
Give that, and lots of people here can help you.
[edit: Just so you don't think I was harping on you here,
I've done the exact same thing to describe the sound I'm after.
But, like you, I can also describe the sound I'm after, or give examples of it in recordings or artists. So I wasn't criticizing your first post. Just asking for more info so everyone here can help. ]