I usually resize to a maximum of 640x480 (or around that anyway) but aim for 500x or 550x for forum messages. I save them at "80%" .jpg using Thumbsplus usually. That keeps them small enough for everyone to enjoy, but large enough to keep details visible.
I would recommend 72 Pixels per inch, your photo editing software should let you select this. In addition I'd save the photo first as a bitmap and the save the resized picture as a jpeg with your new dimensions and resolution.
I usually post either 500 x 333 or 600 x 400 sized pics, usually at 90-93% resolution and 30-50% compression, using the free image optimizer from www.xat.com
Of course, I use print film and the negatives are transfered directly to a CD, so the quality is very high to begin with.
It's my understanding that most monitors have a max resolution of 72 dpi (though a few -- probably Apples! have 90 dpi), and someplace I heard that 640 x 480 is a good basic resolution for net-surfing. So I try to save mine at 90 dpi and 640 x 480 when I post a pic directly into a thread. But sometimes (as you may note in my gallery), I go higher if I really want to be sure that details are captured.