IF BF4 is the game that you really want to play go with AMD CPU and an AMD card. BF4 is optimized for AMD and has support for the mantle API. I don't understand your reasoning on the price to performance ratio with the 650ti. According to the benchmarks that I have seen online using BF4 the 650ti only performed 1fps better than the R7-260 while the 260 is $15 to $20 cheaper than it's counterpart.
If cheap is what you are looking for you might want to look at AMDs A10-7850k APU it has a built in R7 series GPU that outperforms either of these discrete cards by about 5-6fps in BF4 for about $60 less. Also when you have more funds available you can run a R7-250 or 240 in dual graphics with the on-board graphics for a cheap performance boost. Just something to consider
As my name implies I am extremely new to this, but I have spent the bulk of my effort learning about AMD parts because I feel like overall they offer the pest price to performance. Hopefully this helps put a bit though.