Even if you subscribe to HD from Dish or DirecTV you get SD (standard def) channels too- everything isn't in HD.
You should have no trouble recording the SD channels via the S-Video or composite video jacks on a DVD recorder, the hard drive is not an issue. I have lotsa disks burned from an old Dish DVR as well as a current DirecTivo box.
This same DVD recorder could record HD content if the receiver downconverts it before output - but then of course it wouldn't be HD anymore.
A DVD recorder that will record in HD is kind of up in the air right now - they needs recordable discs with higher density - the standard 4.7GB single-layer recordables just would not be enough capacity. I think in a year or so we may see some kind of new recorder/disc technology that will accomplish it. Of course, those will be very expensive to start with, and there will be the concerns by the broadcasters and copyright holders of the programming. I'd expect to see any HD recording gear to probably have some kind of DRM (Digital Rights Management) baggage.