BJ,
consider this: whenever possible, use COMPONENT VIDEO all the way around, in order to get the best picture, followed by S-video & only then by composite video cable.
You've seen by yourself the improvement in picture quality, didn't you?
Another advantage on the compoment video option is that they're 75ohm rated, thus being able for progressive scan signal (you won't get it thru either S-video or composite), but in that case BOTH, your TV & DVD PLAYER must be Progressive scan compatibles.
You've mentioned that your "new" tv set is a 32" flat...
If it's not progressive scan at all and you can return it, get a similar model, but with the progressive scan chipset. Most probalby your DVD player is, so you'll then have a perfect match for the best possible image on the analog domain.
Considering the receiver you have now, the logical way is to connect all your gears into the receiver and then to the TV ( you'll have a much better sound & probably image). In this case, you'll have to run 01 more set of component cables from your dvd to the correspondent input in receiver and from receiver's monitor output to your TV set.
Any doubts, let us know.
Cheers / Avliner