the idea is have at least 8 gbs and as fast as possible, you must have ddr3 with that x4, if the mainboard supports ddr3 1866, that is great, if not, surely you have ddr3 1600, that is ok
about the 960 or 470, i like amd more, so i would go for the rx470, the 960 is rather old and a 1060 would be alot better but we are talking about budget here, also power cnsumption
1060 and rx470 are more close in price, performance and power consumption
is your psu a decen recent psu?
both the rx and the gtx you mention or the one i recommend will require a 6 or 8 pin power connector, not like your 750 ti that uses only pci express power