Recording a jazz trio tips!

[Valloti]

Hi guys, i'm new to the forum and would like to start with "how to record a jazz trio".
Me and my trio are making our first demo, and the new thing is it will be all made by us (me). That means microphoning, locating instruments, preparing the room, recording, mixing and mastering.
It's a guitar (sounding pretty modern like Abercrombie or Frank Möbus through a jazz transistor amp and sometimes a tube amp fender like), an upright bass (me, through a GK mb150s III and hopefully a mic in front of the bass) and a typical drum set (20" bass drum, 12 and 14 toms, 14 snare, Fat old school hi hat and he uses a jack de Johnette crash signature as a crash/ride).
We play a fairly mixed style of jazz with some trashy parts, sometimes a bit of eastern influences and...well very mixed, but jazz at the end. And we would like to get a more classical recording sound, not so hi fi, not so digital.

Any suggestions? and suggestion involving any stage of the recording will be helpfull!
For instance i'm planing to taje the guitar directly from the line out and maybe using a sm 57 for the speaker but i'm not sure which method will work better. For the drumset i want to use the Glyn Johns method, two small diafragm over the drumset (the one on the left slightly down) and a big membrane in front of the drumset, about 50 cm away from the bass drum. For the bass as i said i wanna go with the DI out from the amp (set to pre) and also a big membrane about 40-50 cm away from the bass on the G string side.
Anything there you might want to say?

Recording Through a digital multitrack recorder and then import the tracks to my computer.

For the mix, i don't have a clue yet, i will work either with logic pro 9 or Abletone Live 8.2. I guess Logic is more frienedly and intuitive.
Any MUST for mixing and mastering?

Thanks a lot guys and sorry for such a long thread.
All the best!