The new iPad supports H.264 encoded at a maximum of High Profile level 4.1 at 1080p30 for the video track. The video track can have a maximum data rate of 62.5 Mbps. Technically, the video decoding hardware in the iPad supports up to 2048x1024, but Apple's placed restrictions in iOS to prevent that. The iPad's specifications state that the audio track has to be AAC-encoded at a maximum of 160 Kbps, but I've tried it at 320 Kbps and it works.
If you want to get the highest quality video on the iPad, you absolutely have to encode in High Profile level 4.1. QuickTime does not support conversions to that H.264 specification, so you have to use a program like Sorenson Squeeze and manually specify both the profile and level. Also, if you do decide to use Squeeze, set it to use the MainConcept H.264 encoder instead of the H.264 or x264 one.
Also, set the entropy coding mode to CAVLC.
HandBrake is excellent, but you have to know precisely what to set where or else not-so-good things will happen. :-)