Having used laptops with both ATI and nVidia chips inside, nvidia support is definitely the way to go between the two, especially for multi-monitor setups. I actually returned my old laptop with ATI graphics because their Linux drivers and support was terrible.

I hear that the new Intel graphic chips are also quite nice, and the fact that they open sourced the drivers should make them the ideal Linux graphics adapters, but I don't have any experience with them.

That would have been my answer to the parent: I use an external monitor, mouse and keyboard at home.

I've managed to get the ATI Radeon under Ubuntu to display both two desktops or only use one screen or the other. But it was quite a fight. And more fancy things like one large desktop on two screens didn't work out.

For ubuntu & ati check this http://ubuntuforums.org/showthread.php?p=1773544

if you're using nvidia like me, then it's as simple as adding a couple of lines to your xorg congfig