HD video playback is going to have more to do with:

A) If you can get the file on the server before a timeout occurs.
B) The scripts configuration
C) Connection Speed for downloads

You shouldn't see much buffering provided your download speed is reasonable, and some script players do a better job than others in regards to when they start playback on the progressive download.

In other words it really depends on what your goals are, if this site needs to be usable to your visitors in regards to upload, or just you, who the audience is, etc.

If you want something that will work well for nearly all of your users, a dedicated would be best, if you want something that is primarily for you or a small group then a budget shared pan would work.

If you want something in between, try a semi-dedicated and go up or down in service levels from there.