You will need a non-linear editing system that can handle High Def yes. What i mean by non-linear is that you can stagger clips taken from one peice of tape and that you don't have to cut tape (like they do in the movies)
Right, now HD footage is around 100mb per 10 seconds of tape. So thats a lot of data rate for a system to use. So not only do you need a HD editing suite, but you also need a system that can handle a high amount of data.
If you're a PC user, then get Adobe Premiere (the new one can do HD) or sony vegas. If you are an Apple user (which i am) then Final Cut is pretty much the best HD editing system out there IMO.
You can get Final Cut Express for pretty cheap that does HD editing.
As far as burning goes - you cannot burn HD footage to a regular DVD. It needs to be a HD DVD or BlueRay. Now burners for this are quite expensive, however - you can get your HD footage 'look' onto a DVD. In things like Final Cut, you can down convert your footage to SD (Standerd Definition) and that will burn to a DVD just fine.
Usually, you don't have to have a special DVD burn software for all this as a DVD suite should just put data to disk and not worry about anything other than the size of files - nothing more. The feature that separates a regular DVD from a HD DVD is the capacity of them (as HD takes more data space).
So thats should answer some of your questions. If you have any other queries, then you can get in touch through TheWakePlace.com