An ssd is a must these days as cheap as they've become. The z170 boards support M.2 pcie ssd's and the Samsung 950 pro is the fastest at the moment, here is the 256GB there is also a 512GB.
http://www.newegg.com/Product/Product.aspx?Item=9SIA4P03H20196&cm_re=950_pro-_-20-147-466-_-ProductFor 1080p a gtx 970 is what you want, I wouldn't recommend anything lesser for solid 1080p gaming, getting a free game with it is like an extra Christmas present too.
🙂Here is the 6600k vs the 2600k, he'll gain 10 to 20 frames per second just upgrading the mobo, cpu and ram depending on the game. Add in the gtx 970 over the gtx 770 and there is easily another 10 - 15 frames per second increase. So you're looking at roughly a 20 - 35 frames per second increase with all new stuff. Figure in overclocking the 6600k and the 970 and there is roughly another 10 frames per second.
http://www.bing.com/videos/search?q=6600k+vs++3770k+vs+2500k+benchmarks+youtube&view=detail&&&mid=93...I would also recommend doing the free upgrade to windows 10 for the directx 12 feature, Microsoft says it will be a significant performance increase over directx 11 so figure in roughly another 8 - 10 frames per second. Directx 12 games are coming soon.
The goal when gaming is to keep pegged at your monitors refresh rate which I imagine his is 60Hz which equals 60 frames per second max (with v-sync enabled) without screen tear unless you have a G-sync monitor.
Good gaming hardware isn't cheap, what I recommended is solid for 1080p gaming and is not overkill. Overkill would be a 980ti or titan x for 1080p as those gpu's are designed for 4k gaming and you'd still need at least two of them in sli for 60 frames per second with new games at 4k.
Or as Menthol says he still has a decent setup and he could add another 770 for sli and gain an 80% - 100% performance increase, again it depends on the game or more precisely the game engine how well it's optimized for sli and most games today are optimized for sli, some better than others. This would be the cheapest way with the biggest performance increase if mom is saying no to the gtx 970.
A 750w psu can handle two 770's in sli but wouldn't leave any room for overclocking, finding another 770 could prove difficult though other than looking on E-bay.
As menthol says the difference in performance from pcie 2.0 to pcie 3.0 is negligible.
https://www.youtube.com/watch?v=BopI-XSeMGI