you can do this by purchasing one drive if your in the uk it will cost you about 15 pound delivered.
a samsung 162c ,,,, this drive is a reader only but can be flashed with some modified firmware by a guy called KREON i have the firmware if you need it (please dont post your email address on the forum) once you have done this or bought a drive pre flashed you install it into your pc or if you have a laptop an external enclosure this will now read original xbox games from the standard xbox and the xbox 360 allowing you to dump them on your pc/laptop hard drive.
which then you burn to dvd + r dual layer media (or some standard xbox games to single layer) but these will only play on the 360.
your console dvd drive also needs to be flashed with some modified firmware depending on the drive inside the console it is quite easy but voids the warranty.
backing the game up is a breeze and a very light one at that its simple if you have the right tools