I am definitely thinking that a linux distro would work better and installed on a bootable USB thumb drive, or maybe even a USB3 thumb drive due to the increase in speed.
USB2 works great for most linux distros. Most of the system will be running in RAM, not from the USB directly, so read/write speeds don't come into play often. Especially for a dedicated miner. Only thing to watch out for is if you plan on keeping log files; write them out to a network share instead of the USB drive.
The 6870s are cards I already own, so they are kind of the default to start with. Would there be any problems with me added a 5830 as the third cards in the system?
Your 1000W PSU should handle them pretty well. A really big OC on a 5830 might push 180W / card. Not sure about your 6870's, but I can't imagine it's much more. If you've got a kill-a-watt or something else to measure power at the wall, it's easy to see how much headroom you've got after the 6870's are in.
[edit] Just re-read and saw you're considering 2x 600 or 700W PSUs - this isn't a bad option at all, but I'd do a price comparison. If you're going to have 4 cards eventually, and the power usage of those cards fits in <= 800W or so, I'd just go with a 1000W. If it were 4 6990's on the other hand (350W+ each!) I'd go with multiple PSUs. Remember your max efficiency is going to be around 50-70% of the advertised PSU wattage.
Does anyone have an opinions on the board or the processor to be used? Is 3 x16 slots and no x1 slots worth it? It does have two non-e PCI slots, and I know there are adapters to convert those to x16, but i have yet to hear a consensus good or bad on those cards.
If this is going to be a dedicated miner, and you don't have the components already, I'd look at something with more PCIe slots. 3 * 16x slots is great, but you don't need that bandwidth for mining. You'll find there are much cheaper options with 2 * 16x and 2 * 1x slots, which will work well with extenders. More than 2 * 16x slots and you're entering 'extreme gamer territory' where prices climb quickly.