I need to convert some of my movies and other videos for the iPad and I am wondering what solutions are available for this. Ideally, I would like to have something that adds the new video afterwards to my iTunes.
As for getting videos added to iTunes automatically, that is not something Handbrake will do. If you are using OS X however, this AppleScript seems like it would be up to the task. The script watches a folder, when a file is copied in it waits for the file to stop getting larger (when the copy or encode [in this case] is finished) and then adds the item to your iTunes library. I haven't had a chance to test this for myself though, so I can't guarantee it will work as desired.
I use RipIt to digitize my DVDs, it's dead simple.
RipIt will use a Handbreak extension to compress things in a second pass but I use Handbreak itself for that.
When done I have two files: the ripped file uncompressed which I save on an external hard disk in case OS X's DVD Player ever gets AirPlay so I can play better quality movies through AppleTV, and the compressed file that Handbreak makes which I move into iTunes and sync with my iPad (and backup onto the external as well for safe keeping).
Handbreak is also useful when you want subtitles in a foreign movie or want the extras on a DVD to be available; it lets you sort out the tracks and such although it's UI is a bit overwhelming.
I have a 64GB iPad with over 20 full length movies on it at any one time and plenty of room for more. I fly a lot and the iPad, Bose 15 noise canceling headphones and the movies make long flights tolerable, even enjoyable.
Miro Video Converter is quite good, simple and free, it is a choice.
If it's something you do a lot, you might consider investing in Elgato's Turbo.264 HD, which comprises a USB dongle that accelerates video conversions, and software for doing the conversion (which includes the "add to iTunes" functionality you asked for). The dongle is also compatible with one or two other video converters, such as Roxio's Toast.
You can also buy the Turbo.264 software on its own, either from Elgato or on the Mac app store, but at around US$50 it's hard to recommend... it doesn't really do anything that the cheaper or free converters can do.
Alternatively if you don't wish to convert you can probably play the original video files through an application like AVPlayerHD which supports video formats that iTunes doesn't.