I have recently built a system with a 9590 cpu and a 7870 gpu. I also have an 8350 with 7870s that is currently running linux mint 13 because windows 8.1 rebooted to much. If you don't mind a larger electric bill the 8350 would do some damage on your cpu projects. If your focus is GPU based you may lean more to the FM2 side of things. I like this for a
starter kit and add a different main drive and use the seagate as a backup. This plus a video card and other extras may be over the budget if the software prices can't be found lower. The kit is a rough starting place with rebates and promo codes i'm sure we could get it down a bit more.
I'm not sure Linux Mint is turning out to be all i hoped for, but I prefer the cinnamon desktop even though its not bug free yet. With your office environment needs windows 7 would be a decent choice . I'm not sure you need windows 7 ultimate if windows 8.1 is an acceptable choice. I would probably get windows 7 professional to save a bit of money. I have been using Libre office for my needs, but it may fall short of your current needs.