Hi Mike,
I don't know if you have already planned your trip, but I just saw this thread and thought I could give some input. There are so many "must-see" locations that I couldn't possibly list them all. Check out birdingpanama.com for a pretty good outline of good spots. The three places I would recommend are Boquete - near the C.R. border, Pipeline road - canal zone, and Cana valley - Darien. Close behind those are the Azuero peninsula and Santa Fe.
In terms of accommodation there are a great many places to choose from, and with a little careful research you can find gems (for example casa mariposa in Santa Fe, Ivans B&B near Pipeline road)
For car rental - there are lots of companies and they are of varying quality. I would stick with a large company (e.g. hert,nationa,budge) and avoid the others.
Hope this helps. If you want more info on any place in particular feel free to email me
