Well NVidia Cards work pretty reliable in Linux, the Driver is not OpenSource but its a good driver, only Suspend to Ram is not that reliable with it.
ATI just released their Driver as OpenSource and its supposed to be stable and reliable from what I heard (don't own a ATI/AMD Card).
Of course Intel is always a good choice since their driver is OpenSource for a long time and also very stable and compatible, but since their are no real "Cards" on the Market, you either have an intel Onboard or your out of luck on that one.
All Cards I know of support 1680x1050 resolution (at least the newer ones not older than I would say 2 years) I never hat problems with my 22" LCD running that resolution even an EEE PC can handle it.
I've been running an Nvidia 7600GT in my worksation up until last week (when I sold the worksation) and it was reliable and fast. I was running Fedora/Ubuntu/Arch/Slackware on it and never had Problems, so I guess Debian will be fine
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