I don't have Tivo or a DVR, but they basically have made VHS a thing of the past. You can keep adding to the disc-based recorder and you can program the shows you want to record. The storage is limited though. With VHS you have a copy (lousy copy) that you can keep, but you can do the same with a DVD recorder. The quality will be better than VHS. You can hook a DVD recorder up to the Video-Out of your cable box, or with some fiddling you can hook it up to your DVR to record programs. I don't think DVRs will let you record with either HDMI or component connections, so you'll need to dumb it down a bit and use S-Video. But, it will still be better than VHS.
I'm curious about your second point where you say "I think videotape is more durable/stable than anything I have tried (which has basically been DVD)." Actually VHS tapes are one of the most unstable formats around. The oxide sheds and after a few years you can't even play them. Why do you think DVDs are unstable?
Currently I'm still in the stone ages and still have a VCR,but the quality of the tapes now pales in comparison to what's out there now. The reasons I haven't converted yet are 1)Most of my recordings are all on VHS, 2)I think videotape is more durable/stable than anything I have tried(which has basically been only DVD).
So my ultimate question is what is my best bet to start investing in now? What are the advantages/disadvantages to Tivo or DVR? I currently have DirecTV which may provide DVR.
Another reason I like my videotapes are that I can add things on if I'm compiling a tape,is there anything that can do that? I've heard I can record on CD but if I don't 'seal' it I can't watch it. Again I'd like to be able to compile things.