Re: 3 pedal challenge!
I would take the Fender amp
1. Vise Grip compressor. I cannot rave enough about this pedal. I have had lots of compressors... this is the best most versatile musical awesome pedal! I would use this as an always one, for my jazz gig, and then use it as a clean boost at different levels for the blues and metal gig. It can do some sertious gain boosting, so it works great to stack with an OD pedal and/or distorted tube channel.
2. Timmy (or better yet the 805...but I don't own it YET) This would be the classic tube screamer slot, but I really like the Timmy. I have tried the 805 and think it would be better in this context though, since it is more versatile. The 805 CAN do the low gain, cleanish thing really well, AND can do the higher gain with the mid bump as well... and all the flavors in between. The Timmy has the great natural sound... but that is pretty much it. Either would work for me.
3. EQD Dispatch Master. Yes this seems like cheating since I get a reverb and delay... and it is sort of... but really this pedal is an always on pedal for me. It sounds amazing, and I leave it mixed low as ambiance. It is one of the special pedals that just works SO well. Yes, I can use it as up to a 2 second delay pedal, or a slap back pedal, or JUST reverb. And the reverb can be small or cavernous. Of course, I can also set it to super ambiance settings... and get coooool sounds. A great flexible pedal that never has a bad sound in it.
I think along with a gain channel, I would be well covered for any of those gigs.