It doesn't appear that anyone feels like an expert in this area.
I know nothing about authoring… but it appears to me that all you want to do is burn some movies you took to dvd's.
This comment has me a bit confused:
My goal is to change these dvds and cds to DVD so I can play them in a DVD player and on TV.
Are you distinguishing between dvd's and DVD's? I believe they are the same thing.
You should be able to use about any DVD burning software to do what you want to accomplish. You just need to make sure that you burn them in a format that player of your choice recognizes. I believe that the most common format that your player should be able to play is mpg … specifically MPEG-2. There are many more formats available so you need to see what your player recognizes.