I'm awfully shy about adding my opinions and experiences after such talented bassists have spoken, but here's what has worked for me:
Full Circle Pickup
F-deck High-pass filter
Walter Woods Ultra
Epifani 2x10 or 3x10
Line out to a Radial JDI direct box for connections to FOH
Here's why I think it works:
The high pass filter is not that important to me most of the time but on big stages with rock and roll sound expectations I simply have to cut some of the lows to avoid feedback through the mains. Those mains will reproduce WAY more sub-sonics than anything any of us are willing to lug around, so expect the PA to reproduce low end material that you never ever heard through your amp before. The signal hasn't changed. The amps we carry around just don't reproduce much below 60 hz. That and the fact that many (but not all) live sound engineers think that the Bass Drum is the most important instrument on the stage...)
If your amp doesn't have a variable hi-pass filter built in, then I strongly recommend the under $50 one that Talkbasser F-deck sells. It does the trick. It sounds much better than simply turning the bass knob on your amp down.
The Walter woods head has been talked to death in other threads. Yes it's expensive. Yes there are other options out there now (there didn't use to be!) I double on electric a lot and the woods works well with both.
The Epifani UL3x10 cab is the loudest thing that I can still carry with one hand. Some things sound better for electric bass some things are a little more neutral for upright but this does pretty darn well for both.
I currently don't send a microphone to the FOH. The only mics I like are way to expensive and sensitive to use in these situations- but I'm always looking for one that I like. The above set-up is for sending the pick up to both a stage amp and the FOH. If I did use a mic I would probably use an H-clamp stand and a dynamic mic such as a sennheiser or Heil. Most sound engineers don't want to deal with a mic, or want to take both signals anyway in my experience.
Lastly, I have one more recommendation: Lower your expectations.

Getting a great amplified sound in these sorts of situations is a tall order. Getting a clear (but perhaps not at all natural) sound without feedback is the best place to start. Then worry about sounding like NHOP...