Re: 3 pedal challenge!

Exactly what I use for exactly those genres of music I play. Don't do much jazz though.
This pedal set up works for guitar too. Dunlop Bass Wah, Fulltone OCD, Digitech Bass Whammy.
Edit*
Oh deeper answers... cool I gotcha.
Guitarwise.
I'll take the Fender since I'm more familiar with it, and since I got a clip on headstock tuner lying around so I'll go ahead and use that to keep another pedal slot open.
For jazz I'd use the whammy set at either of the octave harmonies and use it for leads. Don't think I'd use much else. Maybe the OCD for fusion stuff.
For rock I'd have the OCD with pretty much every control around midnight on LP for a lead boost into a crunched amp. Then I'd use the wah sparingly for solos. The whammy would be set to the detune setting so I can have some chorus-like effects to cleaner rhythms, would also be great with the OCD for full and textured leads.
For metal, the OCD is on all the time, HP, gain around 2-3 o clock, same with the tone control (varying depending on volume I can gig with). Wah would be used sparingly for solos too, but the whammy would be kicked in for some sweet harmonies, maybe flex the notes around to shake things up.
For blues, I would do similar to how I would with rock, but a little cleaner, even less wah. No whammy.
Basswise
I'll just use my GK 2001rb, it's only 2 channels too. Got a rack tuner though so that keeps the pedals free of one.
For jazz, maybe a little subtle bass wah for some bass solo stuff, maybe a little whammy on the detune setting too for effect.
For rock, the OCD would be on HP with the volume high and the gain kind of low, just to add some gritty texture and harmonics. I wouldn't do much more than that unless it was prog rock, then I might use the other pedals to fill out some atmosphere.
For metal, the whammy is my secret weapon. In my 1 guitarist band, when he goes to do his leads live, I can throw that on to support him more so the band doesn't lose any sonic weight to it. Usually set it to 5th or either octave harmonies. OCD, everything a little past 12 o clock at HP for a distortion boost, the amp usually has a bit of grit dialed in anyway so it is mostly for fuzzy effect. Wah occasionally for general effect. (For rock and metal, sometimes I will set the OCD on with a setting that actually is quieter than the clean amp, this way I can switch it off to take the grit away and let the full clean volume come back in for parts where only the bass is playing, maybe with some drums. This way, in songs similar to say YYZ, the gritty bass mixes well with the guitar when both are playing but when it needs to be pushed up while lifting OFF the grit instead of putting it on, it can. So I use it as sort of a CUT pedal instead of a BOOST pedal sometimes.)
For blues, I'm just going in clean. Can't see myself using many effects there for bass.
In general, I like to use the octave harmony on the whammy and some OCD distortion to get synth like tones out of both instruments. It's fun to play around with.