I tend to set the height of the bridge based on the banjo. I have a higher bridge on my Hartel, and the thumb string/bass side is a little higher than its oppsite. This is because my bass string sometimes buzzes when I really strike it hard. I still have a very close string action up on the neck, so the high bridge doesn't had any adverse effect.
On my Wunderlich hybrid (I made the neck), after re-doing the neck recently, I have a much lower bridge than I used to. (The string action is now much closer to the neck than it used to be.) I was having some of the stability problems Tim mentioned with this one, the bridge wanted to bounce around a little. I ground up some rosin powder and put that under the two feet, and that solved the stability problem.
I make a bridge or two every day. Today I made 5.
Pine is best. If you have Nylguts or gut with a wound 4th, poplar is best because in time the wound 4th is gonna dig in. I would even guess the softer bass for a gut set, I have used basswood for guts and the sound is great.
I have a method for determining bridge height. I tune the 4th down to Gb and hit it hard - if it rattles on the fingerboard the bridge is too low. If it doesn't rattle tuned to Gb it sure won't when tuned up to G.
My banjos have about a 1 1/2 - 2 degree neck slant. The originals hardly had any. Modern guitars have 3 degree.
I like a big round sound with clarity. I want it all. This neck angle puts a pressure on the bridge that brings out the volume but keeps the bridge 'afloat' on humid days, in other words the skin sinkage is minimal.
The old bridges were thinnish.. I like the looks of them and the violin bridge principle that the feet of the bridge is 2, at the most 3 times wider than the thickness at the top. If the feet are too wide your banjo will lose its midrange somewhat. If you want more boom on the bottom, make a bridge that is thick overall. And like Carl said, a taller bridge for more volume.
The main thing I keep in mind is the dreaded sinking skin or rattling string for whatever reason, and some of that reason is the adrenalin factor. It feels good at home but it gets rattly sounding when playing live because of your natural exitement and hitting the strings harder. So whatever material, thickness, position, or angle, I always keep the bridge a little on the tall side. Everyone loves the feel and sound of my banjos, so give it a try.