Question: What would be the most cost-effective way to go about this? My friend told me that it wasn't as simple as adding a second identical card for 3 more monitors, and that I need to buy a new $500-1000 graphics card
Question2: If I decide to stop at 6 monitors, would I be able to run two radeon 5850's separately, with a shared desktop? Someone told me I would run into issues with this but I didn't bother to ask what they meant.
A 5850 will run up to 3 monitors, I've done it. You don't need or want an identical card for crossfire because you'd still be limited to 3 monitors. Your best bet would be to buy an eyefinity card that supports 6 on it's own, then you could run the two cards in tandem (not crossfire) with 9 monitors.
There aren't a lot of 6 monitor cards out there, though, and they are pricey. I remember there was an Eyefinity 5850 and 5870. For 3 monitors just running desktop/2D stuff, even a 6750 or 6670 should be fine. If you plan to watch a movie or game a little just run it off the 5850.
As others have stated, you don't need or want another 5850. Your cards only have to be the same when you're using crossfire. Crossfire treats 2 or more cards as a single card for increased performance, but you only get to use the displays from 1 card, and you don't need a 5850 to drive monitors.
This XFX hd6770 looks like it supports 5 display port monitors. If your monitors don't have display ports, you'll need active adapters.
Have you checked how many extra PCI express slots your motherboard has?
^Right, but looking at crossfire 5850 power usage when you are considering a 5850 + 6770 (or less) isn't very representative. 650W will be plenty for what you are considering. Also bear in mind those power charts are "at the wall" so if you factor in efficiencies and such, let's say they were using an 85% efficient PSU, then the actual PC power usage is only 468W.