I used to do a lot of live sound engineering - mostly on the monitor desk, but I was still involved in running the set-up.
Vocals and drums need mics obviously. Guitars are next priority for mics because a large part of the tone comes from the speaker.
If the bass was running through a rig that obviously coloured the tone (vintage fender, marshall, vox ac-50, etc) then we'd stick a mic on one of the cones and take a DI from a box before the amp - mainly run the DI through the PA, but with some mic to add the "flavour" back in. Mostly we saw Peavey and Trace Elliot stuff so we'd DI from the amp head because we knew they were acceptable DIs. Any probs during the soundcheck and we could stick one of our DI's in instead.
I only remember one arrogant bassist who came on for the gig, unplugged from the DI box and went straight into the amp so we only had the mic signal. Because of the venue acoustics I couldn't let much of his signal go through the monitors without feedback (the FOH guy had the same problem too). He spent the whole gig moaning at me that he couldn't hear himself in the monitors, I think he'd have been even more upset that there wasn't much of him in the FOH mix either.
If you wanna get listened to buy sound-guys (or gals) learn to speak their language and learn a bit about acoustics. Secondly, as soon as you've got the gig, find out who's doing the sound and send them a cd/tape/mp3 - that gives them a bit of time to think about how to represent the sound of the band.
The other option is do what we've done and get a sound guy to join your band - he gets a cut of any income, but in return has to come to rehearsals so he knows our set as well as the onstage members and can also discuss problems that he foresees as they arise. Works well for us.
Final tip is don't forget its not your sound once its in his PA its HIS!