I think you may need some extra steps before going to PA.

I have played medium sized indoor and outdoor gigs with amplified mandolin, and I would say that feedback control is essential. Straight to PA hasn't cut it for me in some situations.

Most piezo pickups for mandolin - bridge or stick-on bug - are very prone to "pick thud". Microphones (the best option for good sound/tone and faithful reproduction of acoustic sound) are prone to feedback.

If you're going to plug into a PA then I'd suggest a good preamp/DI box - something like a Fishman ProEQ Platinum or Baggs Para Acoustic. Both of those have phase switches and notch filters which do a very good job of controlling feedback.

Instead of, or as well as, the preamp, a good acoustic amp is a real benefit. I recommend the Marshall AS50D, or the 100 watt version in the same range. Great little amps which feature the same feedback-busting measures as the two preamps I mentioned above. The preamps and the Marshall amps also have XLR inputs and phantom power. Your SM57 would plug straight in.

Another mic worth checking out is Shure's PG81. A reasonably priced, small diaphragm condenser mic. Great for mandolins - I use one regularly.

Hope you find what you need.

As for mics,