X51-R2, graphics card upgrade

It all depends on the power supply you have. There were two, a 240W and a 330W. With the 240 you would have to upgrade the PSU for almost any GPU upgrade. With the 330W you could not use the  970 which requires a 500W PSU but you could go to a GTX 1050Ti. The 960 and a GTX 1060 both require a 400W PSU and might work. Looking at the specs for the card you have now (660) Nvidia calls for a minimum of 450W with a 6 pin power plug.  If your 660 runs now then the 960 or 1060 should work.

NO.  Upgrading the power Brick to 330W will allow a 1050TI which is as good as a GTX 680.

Zotac GTX 1050 TI Mini is the recommended part.