I recommend the Swollen Pickle. I got one last Christmas and I will never replace it(unless I need a new Swollen Pickle). Its awesome and when you get to a point where its not loud enough, you can mod the internal controls. Usually when you have to go inside, you can find what you want in ten minutes.
-For songs with more high end, you want less filter and scoop and more crunch and sustain.
-For your dirty low end songs, you want the same high end crunch and sustain but more filter and scoop.
-WARNING: that thing gets LOUD. The loudness is something that you crank up when you are outside and/or playing for a big crowd. its not the thing you want to "crank up to 11." If its not loud enough, leave the external dial where it is and go inside to turn it up.
-not for the prude, elderly, weak or faint of heart.
I voted "fuzz", but for your first fuzz I would start with something a bit more tame than the Swollen Pickle. Take "not for the prude, elderly, weak, or faint of heart" as the gospel! So my setup basically encompasses everything you're thinking about: I run a MuTron III+, a Boss BF-3 Flanger, a couple octavers (OC-2 with normal plus 1 lower, MXR BOD with just the low octave passing through), and a Fulltone Bass Driver and most recently- just in the past month- the Swollen Pickle.
I am having a hard time getting the Pickle to play nice with the other effects, like the MuTron and octavers, if does sound sweet feeding into the flanger. I find that too low, in a "textured" use, the Pickle just dies on the bandstand. Crank it up a bit - to the point that when you solo it alone it sounds *ridiculously* too loud - and in context on the bandstand it reaches out grabs attention like nothing else. So I am a pickle novice, YMMV, but...
I use my Fulltone set to a very mild distortion, actually on the "Clean Comp" setting, although it's not really clean, it is very subtle alone. But it does make every other effect "pop" a lot more. It's awesome with the MuTron, the Flanger, and either octaver. So I would suggest getting a fuzz that can do some lower-intensity stuff well, although go for something with more bass preservation than the Bass Driver, maybe a Pork Loin? Maybe the VT character pedal?
If on the other hand you just want to melt faces, then the Swollen Pickle isn't a blow torch, it's a blast furnace. All of this represents my personal experience, with an active bass into a Mesa/Genz rig (pretty full-range but EQ'd to a round sound).
Another contender for "set phasers to melt" is Fulltone's OCD, but I found the Pickle to have *a lot* more tonal options and variations, but the OCD was easier for me to dial in effectively on the gig and played better with the MuTron. There's many faves I have not personally tried but would if I could: Pickle Pie B, Red Ripper, Iron Ether's fuzz pedal (Iron Oxide IIRC?).