Geminii S is not tall enough for RipjawsX, but not too wide to block the innermost memory slot (hopefully, depending on you mb). F3-1600C9D-16GAR or F3-2400C11D-16GAB (2 x 8GB, more memory is better for your purposes) is a better choice.
Intel ATX high-end system should be good, with this graphic card (2GB video RAM). I am not sure how much improvement you would get, however. SSD, HDD, PSU and case can be reused, of course. Geminii S (older version) requires RR-ACC-1156-GP retention kit to install to LGA1150 socket, however.
Gigabyte Motherboard GA-790XTA-UD4 spec says max 16gb of memory, can I use this kit F3-1600C9D-16GAR you recommend if I remove existing memory? Or am I limited to max 4gb per slot? Thanks again!