What is the best format to save these videos in?
YouTube and Vimeo both currently recommend H264 (MPEG-4 AVC) video compression and AAC audio at 24, 25, or 30fps. You can find compression how-tos from YouTube and from Vimeo.
If you are planning to serve the video yourself (instead of from a third-party service such as YouTube), you will likely have to compress and serve multiple versions of the same video in different formats, depending on what codecs the visitor’s browser supports. Mark Pilgrim’s ‘Video on the Web’ tutorial goes into much more detail, and reading it will probably encourage you to use a third-party video hosting service who will handle the technicalities for you.
My advice with Web video is almost always to use a third-party video hosting service so that you don’t have to reinvent the wheel, and so that you can spend time producing content instead of working out how to serve it.
(You say your other questions were answered in my comment above, but let me know if you need any more information.)