Only reason to increase ram would be if you know tour doing video editing or virtual boxes, things like that, otherwise its just a waste of money
Also, haswell memory controllers are touchy so you wouldn't even be able to tell if it would work unless u bought and tried it
With haswell less ram sticks = best chance of it working if you are going to edit and things like that by all means 32gb it up, if not 16gb (2x8) should be good
As for your HDD issue you can do it 2 ways, I play heavily heavily nodded games like fallout 3, fallout new Vegas, skyrim, etc.
A guy who's videos I watched named Gopher uses a very large ssd for his games to give them the best possible speed
But if I recall correctly ssds aren't ment for that, the multi access and paging isn't what it was intended for
The setup I plan for myself should work just fine as well tho, I have 2x 840 evos 120gb in Raid 0, planning on adding a 4tb WD black series drive which is supposed to be one of the most reliable and fastest mechanical drive available and I plan to use that as a backup/storage drive
Typically CPU,GPU and ram will effect games more then HDD speeds
Also the corsair cooler should work fine, just be aware that the corsair link included with the I versions will cause issues if installed on a PC with Asus software
CoolerMaster HAF 932 Advanced/ Maximus VI Formula/ I7-4770K/Swiftech H320/ Corsair HX850/ G.Skill Trident X (2x8) 16gb 2400MHz/ 2x 840 EVO 120gb(Raid 0)/ WD 1TB HDD (Backup/Storage)/ EVGA GTX 1gb 560 TI/ Asus 12x bluray combo