I guess you are talking Windows machines as Quicktime + Flip4Mac (registered) plays and converts AVI and WMV videos to iPhone or iPad video formats. I guess if you register the Quicktime on the PC it will allow you to make the conversion.
You are asking for what video format: Use H264, the files must have the m4v extension and use the same resolution pixel x pixel.
As for Handbrake it only rips DVDs and it doesn't convert from one format to another. For video conversion on PCs I will do a search for Free apps first, as there are several apps at around $30 that convert videos.
One thing I always recommend is if you have the DVD disks is way faster to rip the DVDs to an iPad format than to make the painfully slow video conversion. This is slow no matter what program you use.