All you need is CPU + Mobo?
For around $150+ you could get a Haswell i3 + a cheap LGA 1150 motherboard and it would leave room to upgrade to an i5 or i7 later down the road. A Haswell i3 would be more than enough to keep up with the HD 7770.
*But if you could spend that much, might as well get a Skylake i3 + LGA 1151 mobo. But this all depends on what RAM you plan on using.