Questions about my tv and buying a dvd player?

I have a new big-screen HDTV that is capable of 1080p, on the way. Sony Bravia KDL-40V4100. My family is old-fashioned and way behind the times in technology. All that we have is a 4-head vcr and a ton of VHS movies. I got a huge discount on this tv through my employer (by the vendor), so I went ahead and got a flat screen 40" tv. It was $600 bucks after taxes. They probably never will get HDTV (at least not right now), but I wanted that option there if they ever do.

I'm planning on buying a combination 4-head vcr/dvd player. I figure that maybe I should just get a combo vcr/dvd burner while I'm at it (it's not much more in price). For one reason...just to save some space later on, I figured that we might want to record from VHS to DVD and ditch the clunky VHS tapes - while keeping the movies. I know that the quality from VHS will still be VHS - even if dubbed onto a DVD, of course. But I have a couple of questions: Can all DVD burners record onto a dvd directly from the tv? I know that many record from VHS to DVD and vice versa, but I've only seen one so far that said you could record directly to DVD from the tv.

Keep in mind that my family doesn't even have cable - they use regular tv reception with rabbit ears. I just wanted to get them a thinner tv that was larger and easier to see. A blu-ray player is definitely not something we'll be getting. So what is my best bet for a dvd player? Will 1080p 'upconversion' dvd players look better on this tv than the typical 480p or whatever it is that regular dvd players play? Or would getting an upconverting dvd player (to 1080p) be a waste of money?

Secondly...what exactly is 'upconverting'? Is it beneficial to have? I'm confused as to how one can see a "1080p" (or 1080i) picture from like a 480 (or whatever it is) picture quality from a regular dvd?