If you have an integrated graphics card, you technically would only need to add one graphics card with dual monitor support to obtain the functionality you need. You can use some of the money you saved to get a very nice monitor. :)
You could put that in the x16 slot, or in the regular slot; I'd use the x16 slot if your'e into CAD.
If your integrated graphics card is disabled when you put in a new PCI-E card, you really don't have much of an option: you'll have to get two cards, with a minimum of three video outputs for monitors between them.
As for which chipset to get, I'm not sure if this is really that big of a deal if your'e doing non-graphicsy things. My Linux guru friend says that ATI cards aren't very stable on Linux for anything other than basic 2D work right now. If your'e doing CAD, you'll need to make sure you have a card that provides graphic acceleration support for your applications, but other than that, I can't think of anything.