Hi cuchosan and welcome to the Q&A Board!
What a wonderful project!
As to PictBridge, almost any digital camera you by today is pictbridge compatible. I've recommended the following camera (or one of it's successors) more than I can count. There is so much packed into the camera for the money. I've personally owned and used 2 A Series digital cameras.
This model has a 2.5" screen, veiwfinder and manual controls...though plenty of auto and scene modes. It has image stabilization and face recognition too. Very fine image quality and exposes well.
The Canon A590 IS:
http://www.amazon.com/Canon-PowerShot-Digital-Optical-Stabilized/dp/B0011ZCDKSI'm personally not aware of any cameras that use blue tooth, but there are wifi cameras which I suppose doesn't help. If so, Kodak, Nikon and Canon all make wifi digital cameras. Nikon makes the least expensive WiFi cameras that I'm aware, such as the Nikon Coolpix s50c.
Kodak makes a wi-fi card for some of their cameras:
http://www.amazon.com/Kodak-Easyshare-Digital-Camera-Printer/dp/B0007KQWFU/ref=sr_1_1?ie=UTF8&s=electronics&qid=1238264426&sr=8-1The best thing to do is a search Amazon or similar site for what's currently available and to find one in your price range.