DVD Shrink should be all you need after your DVD burner and burning software. You don't need 2 DVD drives if you have enough space on your hard drive to hold the temporary copy.
Storebought DVDs can be up to 9GB large. Up until recently all burnable DVDs were limited to 4.7GB. The new "dual layer" ones will do 9GB with the dual layer media but are more expensive.
DVD Shrink will shrink the movie (if necessary) to fit on your 4.7GB disc. It takes about an hour or so for me to back up a DVD with DVD Shrink. There must be detail loss, but I haven't noticed it yet.
Since burned DVDs can't have CSS encryption, the copies will not be encrypted and should be copiable using your regular DVD copier software.
DVD Shrink can also make the copied CD so you can skip the previews/ads/fancy menus if you want to.
DVD Shrink is free. Woohoo!
If you want to learn more check out http://www.doom9.org
, but there are many topics and many tools discussed and they get pretty detailed.
It's nice to take the copies on a trip with the portable player; I don't have to worry about breaking the originals on the plane.