In my own experience, mics for PA use and mics for studio use aren't hugely different. A good microphone is a good microphone. My own personal favourites that I've used are:
Overheads: AKG C-1000
Snare: Shure SM58/57
Bass: AKG D12 (D112) (I would like to use an Audix D6, but no experience with sadly)
Those are a good 'industry standard' set to work from. Obviously the prices might be a little high (especially for the overheads) but that set works and has been shown to work even in inexperienced hands like my own with sub-par (even for an amateur) skills and almost no experience.