Both MC and handbrake will likely take a long time to convert/shrink your MKVs to iPad format, whereas in reality, the chances are that the video is already h264 (most MKVs are) and the ipad will handle those just fine (with a few caveats)
If this is the case, you simply need to remux (re-package) to the right container (mp4, m4v, etc), and potentially select or convert the audio stream (it won't do the higher end multichannel stuff - DTS etc) to something the ipad will play; e.g. 2 channel AAC.
I'm not aware of the equivalent windows tool (although I'm sure it exists) for doing this, but in the mac world "subler" is the go-to app for this kind of thing.
It also grabs/embeds metadata/subtitles for your media, and imports into iTunes for you ready for transfer, and I highly recommend it
Simply stripping out the high quality multichannel audio can significantly reduce the file size too, without losing any image quality.
Alternatively, if you have a few spare dollars, you could try AVPlayerHD on the iPad from the app store.
It plays MKVs directly, and often is able to do h264 hardware decoding just as the apple video app does.
It also streams videos from your PC too if you are capable of setting up an ftp server and are happy watching at home on your wifi connection.
It did recently drop support for DTS audio though (due to licensing costs) but handles AC3 just fine.