All I record is jazz. I record my own group where I play double bass (upright bass). A lot is going to depend on the room, and the ability to monitor what's getting in to the mics.
Benny is right on with the drums. A stereo pair and maybe a kick. I like to add a mic on the snare in case the drummer is using brushes a lot; brings out that detail if you need it, especially if there is a lot of audience noise. I have my best luck with a spaced pair coming from behind the drummer, like on each side of him - BUT NOT TOO HIGH! Get them as close as possible while still keeping the kit balanced (and not getting hit by the sticks).
I would probably mic the guitar amp the way you would for other styles of music. Sax, a really good dynamic or a small diaphragm condenser clip on if you have one.
Double bass is a bi#ch to record well. If the player does not really dig in and play hard, it can be a quiet instrument and the mic picks up more drums and other stuff than bass. It can also be hard to place a mic close enough where it won't get bumped, or he won't move away from it too often. Generally, the best place is around the soundpost (near the bridge leg on the G-string side which is to the right if you are facing the bass). DO NOT mic the f-hole. You will get nothing but wolfy mud. I use a small clip-on condenser for mine. If you put a mic on a stand, use the one you have with the best off-axis rejection and the least off-axis color. What qbert1 said is good too. You can get a good sound by jaming a mic between the bridge legs or tail piece when you wrap it in a towel or foam - but that one can really depend on the bass / mic / player, etc.. There will be plenty of other stuff bleeding in that mic. Accept that. Mic the cabinet (if he uses one) or take a direct signal, but use it VERY sparingly in the mix, if at all. Watch for phase issues between the bass mic and the drums, since they will be your greatest source of bleed.
On top of that, you can try to place a stereo pair somewhere as if that was your only way to go. Find that sweet spot. Get a good recording that way and add the other tracks only if they are needed.
Good luck. Let us know how it goes.