That power supply doesn't appear to have a 6 pin PCI express connector which your video cards require.
With the GTX 970 the game can be run on the fullest settings (including environmental slider) and hold a steady 60fps.
Standard power supply will extend about 5.5 inches into the computer from the rear. If you have that much room it should fit.Be sure to read the customer reviews. That Apevia has some really bad amazon reviews, Newegg reviews are bad too.
Just a heads up. When I was testing AH3 it never got even close to using 3GBs of VRAM. The highest it got for me was just under 2.3 GB and that was with maxed out graphics. Obviously lower graphics setting would mean less VRAM used. So a 3GB card can work with AH3.If you plan to play other games besides AH3 then 3GB might be trouble in some games unless you turn the graphics down a bit. The 6GB version you listed should be more than enough to max out any game easy.
Power Supply: http://www.evga.com/Products/Product.aspx?pn=100-W1-0500-KR
That looks like a pretty nice power supply
I've got an older system by today's standards that still runs the game well by my standards.
Vraciu, it looks like you've been through a learning process during last night! The last decisions start to look like you might get a working system for a decent price. Nothing fancy but probably worth the price.