The Z97C and K are ATX motherboards, so they are physically bigger and have more slots. If you are thinking of adding a second video card at a later date, you should go with one or the other. Beyond that I’d have to delve. But it does mean that the whole box will be bigger. This can be advantageous for cooling, but the disadvantage is the increased size.
EVGA have a superlative replacement and maintenance policy. You do pay for it, though.
Absolutely do NOT go for the generic PSU. The Thermaltake Toughpower Gold 550W PSU has been well-reviewed. Do note that 550W will be enough should you decide to add a second GTX 970.
Sorry, I can’t help you there as I use a trackball.
In response to the OP’s problem of the machines just shutting down: I have a friend who has had this problem twice now on her laptop. Both times she insisted it was a problem with the OS, or a virus. Both times I opened up the machine, and blew all of the cat hair off the heatsink with compressed air. This might not be what the OP’s machines are suffering from, but it’s worth having a look.
Overheating was my first thought as well (I had an earlier computer that had this problem, only instead of locking up, it shut the computer down as if somebody had pulled the plug), but after cleaning out the inside and the fans, it still had the problem.
Update: I got one from Cyberpower - only to discover that the 970 video card only has a DVI port, and my monitor only supports HDMI and VGA. Looks like I’m off to Fry’s this Saturday (and failing that, Monoprice on Cyber Monday) to get an HDMI to DVI cable. (Do these things work, or am I much better off shelling out for a new monitor? My current one is a 27" Samsung, and I don’t have room on my computer desk for a larger one.)
I checked the online prices at Fry’s, and discovered that, even after shipping is added, I can get it cheaper through Monoprice, especially as I could use another cable as well. That’s one less store I need to go to.