[dba-Tech] Question about cable tv and recording therefrom

I subscribe to an outfit called Rogers. I have a box somewhat like a TIVO
but less intelligent, I think. It can store about 45-50 hours of programs,
and some of the diagrams in the manual indicate how to record captured
programs to VCR (which is about as useful as recording them to 8-track or
BetaMax). The whole 45 hours is almost full and I want to burn said captures
to DVD. None of the diagrams in the manual indicate how to connect a DVD
burner to this box (Scientific Atlanta 8300). There are standard RCA outs
but I am under the impression that I will lose lots of quality going this
route. I could be wrong. 
The local store has a VCR/DVD recorder and the guy there assures me that I
can burn a DVD from the Scientific Atlanta box to DVD, but with the
following proviso. I must select a saved item, then play it and capture it
from the play. No reason to doubt this... just that I do NOT want to waste
time figuring this out. The VCR/DVD unit is stereo, and so is my TV, and so
is the Scientific box. Since I haven't yet purchased the VCR/DVD unit, I
cannot describe its back end. It seems entirely pointless to me to purchase
a combo unit; I do have a collection of VCRs but so what? I already have a
(mono) VCR player, and those VCRs that I do have and treasure I will happily
rent their DVD equivalents and burn them. But I have about 40 hours of stuff
on the Scientific Atlanta box that I DO want to save to DVD.
Has anyone achieved this? I have three DVD burners already, installed in
computers that are about 20 feet from the Scientific Atlanta box. Do I need
to purchase another one to live right beside the TV, or could I get a
25-foot wire and pipe the output to one of my PC burners?
(Aside: everything I want to burn comes from one creator, a certain Chris
Haddock, who is IMO the best thing that ever happened to CBC drama. If CBC
would only create some DVDs I would happily buy them and be done with it,
but for some idiotic reason CBC has not done so... so I am stuck with making
my own. I have no intention to violate copyrights, mass produce them, etc. I
just want to watch them repeatedly.)
So, what do I need to buy to achieve this?
TIA,
Arthur