Last thing I want to do is a « no effects » trolling thing but... the first step to even string volume is to adjust pickup height properly. I get a very even string to string output even on my G&L L-2500, which has a very strong low B sound, since I adjusted the pickups putting them slightly further from the string on the low B side, specially the neck pickup.
Then EQing helps too! Spot the frequencies that become invasive with some strings but less audible in others and even out the whole thing!
When you’re done, if you still need a compressor to even out
your sound, don’t expect consensus here on a specific model
I use TalkBass for inspiration mostly, then go with what people suggest to organize my own tests and trial and error.
As far as compressors go, I do use one mainly to tame some of my envelope filters and my fuzz (the Bass Big Muff’s limited blending capacities become more useable when you squash the signal afterwards, but that’s another story) as well as to compensate for my occasional excess of enthusiasm when I slap’n’pop!
My choice is a simple ART Tube MP/C. Tube preamp (more on the modern warm side) and compressor with just a threshold control + speed and slope switches. I find it doesn’t kill my tone and does it’s job. Should be under $100 in the US, as it costs $109 in Canada.