My opinion. Been playing bass since 2003 or so, and semi professionally from 2017-2020.
P bass: foundational. Hits like a hammer in a mix. Tonal variety comes from using different plucking techniques.
J bass: lower lows, higher highs. Works better in a sparse mix than a P. Tonal variety comes from blending pickups. Mid scoop when you put both pickups on full volume... knock one pickup's volume down to restore the mids.
PJ bass: basically a P bass but with the option to get tonal variety from blending pickups.
Stingray: bridge humbucker so you kind of know what you're getting. Fat nasally tone. Sticks through a mix well.
Beyond this there's a wealth of information on Talkbass, Gear Page, Youtube, Google, etc. Bassists will fall over themselves to tell you what they think and give comparisons.
Biggest suggestion from me is to think about how you want to use the bass. Do you see yourself honing in your right hand technique? If so, P Bass will do great. If not, PJ/Jazz/Stingray. Personally I find Jazz basses to be weaksauce in my hands, but sound great in others'.
I agree for the most part. But I'd also add a Thunderbird bass. Dark and thunderous.
But depends on what kind of mix we're speaking of as well.
For a more metal mix, I find J-Bass sits better than a P-Bass because it's got more clank to cut through, and a lower low-end to fill out below the guitar's chuggs. Honestly, for anything heavy other than like Maiden, LOL.
Also, the stingray pickup is more of a middle pickup rather than bridge, IMO.
Also, there are other bass setups. Especially if you're going for more of a modern tone. Dual humbucker basses, basses with a pair of J pickups closer together.
I do love me a good classic Jazz bass tone for metal, but also, don't discount Spector and Warwick.
Also... LEMMY!!!!! Rickenbacker bass played with a pick ran through a distorted amp can sound killer.
But then, I'm the kind of guy that can't play without a hint of overdrive in his bass tone. And also, I prefer the sound of a bass being played HARD with a pick rather than finger style. JMO. And I'm more of a guy that likes clank and rumble rather than growl. Growl can turn into honk fast. But as you can see, I like heavier bass tones rather the the dark dum dum dum tones in reggae or more old-school music. I hate old strings on bass.