PVR's don't record anything from the TV, they have their own built=in tuner(s). So do you have a true PVR that records whilst the TV is off and will record up to 2 programmes at the same time as well as allowing you to watch a third that was previously recorded?
If it's a true PVR then it's only SD (as opposed to HD) and will record only SD channels. It won't even tune into the HD channels as they use a different transmission method.
So the TV that's attached to the PVR doesn't have any effect on what you are recording. Therefore you can use an HDTV without a problem but it will only show SD quality definition as outputted by the PVR.
You should connect the PVR to the HDTV with a SCART lead and that will deliver SD quality pictures.
If you want to record HD quality you will need a PVR with HD tuners and these are still expensive.
If you really want HD quality pictures then consider Freesat which is Freeview delivered from a satellte but has a wider range of channels and has much more room for HDTV.
To receive the widest selection of HD prgrammes you will have to have Sky. They currently have 50+ HD channels whereas Freeview has only 2 at the moment (and only room for 5 in total).
So not quite that simple!