I find that I'm sort of the other way around, rather than pursuing a sound in my head, the sound seems to drive me.
I pick it up and I play it, and the way it sounds makes me play a certain way. If it's clean and sweet, my early classical guitar training takes over, and I catch myself using arpeggios and vibrato and being more melodic, whereas a different sound might put me more in a motown groove.
As for effects and amps and whatnot - I used to work for Precision Audio in Los Angeles, at one point maintaining installations at The Roxy, Gazzari's, The Whiskey and The Palace, while also building big road rigs of anywhere from 5kw up to 50kw, and after having started on an Acoustic 360, then gone to a Sun Colossium, then a pair of SVTs and eventually arriving at a pair of GK800RBs matched with a pair of GK 4412s (4x12 reflex loaded, 2x10 front loaded), I ultimately ended up getting away from bass amps altogether and just using a cut-down PA rig - Crest Audio stereo tri-amp (2 @ 500wpc, 1 @ 100wpc), Precision Audio boxes w/Emilar speakers and Emilar horns with JBL drivers, 2x15, 4x10, 2x2 horn.
One of the main benefits of using such a setup was that I could send the signal out of my rack to the snake head, then catch a return off the board into my amps and I would hear the same bass sound that was being sent to the mains.
I could also catch a monitor feed and mix that in to my amps if I wanted to, and since club montiors were always worthless, I would normally do that when playing a club.
To this day I still prefer to just use a clean PA for amplification and though I haven't played a stage gig for years, for practice I use a little Yamaha PA with one 250w per channel stereo amp and two boxes, each with a single 15 and a 1 horn.
As for effects, I am a well-known and notorious gear thief. Over the years guitarists especially have learned that when something is missing from their rack or pedalboard, they should first look to see if I've patched it into my rig. I've been known to run chorus/flange, comp/limit, eq, aural exiters, pitch followers, spring reverbs, distortions, delays - anything I can get my hands on I'll patch it into my rig. I've used Leslies then miked them (I love Leslies). I've taken stick-on drumhead mics and stuck them to my bass. I used a talk box (I liked it, but I would drool too much). Ebow? Yup, bought one of the first ones that came out - awesome.
When the Sonic Maximizer first came out, I tried it and it was cool, but it seemed to me that it would be better to use it on a PA than on some stage rig. Mine was mono so I swiped a stereo model from a keyboard player and patched it in between the mixing board and the mains on a 4kw club PA. I had to tweak the timing a hair as bodies filled the room, but it was excellent, but I stopped using mine for bass after that.
I like amp/speaker rigs where the spectrum analyzer matches what the tone generator is doing as closely as possible, then I prefer to do whatever signal processing I'm going to do before I send it to the amps. But when it comes to processing that signal, anything goes.