Hi, and welcome!
3 models to consider...
451S - 4x +R, 4x -R
851S - 8x +R, 4x -R
812S - 8x +R, 8x -R
Except for their maximum DVD-burning speeds, each is roughly the same (same reading performance, same CD performance, etc., etc.)... the one exception is bitsetting...
) 451S/851S support bitsetting... 812S does not support bitsetting *yet, but it will in the future with a firmware update
*) People who really want bitsetting for the 812S have temporarily "downgraded" the 812S to a 851S by loading a 851S firmware onto the 812S... it gives them bitsetting, but causes them to lose 8x -R (only temporarily... once they restore the 812S FW, they'll regain 8x -R)
Personally, I'd go with the 812S. Have heard of many people with great experiences with this drive. It's a great drive.
(411S/811S omitted... they're priced the same as the 451S/851S, but the 451S/851S is better, I think... plus, it's getting hard to find the 411S/811S nowadays anyway... most people who try to buy them end up getting sent a 451S/851S)