You definitely want to get the R7 250X, since it is essentially the updated version of the 7770.
What resolution and graphical settings are you going to be playing BF3? To achieve 60 FPS with an i3 4130 and an R7 250X, you're going to have to tone down a lot of settings.
Also, what's the exact make and model of the PSU? If you don't know or can't find out, please take a picture of the following label on the PSU and post it here: