See this thread: -
http://www.tomshardware.co.uk/forum/id-2506073/amd-radeon-260x-1080p.html
Also here are the benchmarks: -
http://www.cpubenchmark.net/cpu.php?cpu=Intel+Core2+Quad+Q9550+%40+2.83GHz
https://www.cpubenchmark.net/cpu.php?cpu=Intel+Xeon+X5450+%40+3.00GHz
http://www.videocardbenchmark.net/gpu.php?gpu=Radeon+R7+260X
I have a 750 Ti OC in an old machine that scored 4751 in that test and it performed well at 1080P with High or even Ultra settings in most modern games. You are going to be a fair bit below that with a r7 260x though.... but 2GB vram is fine for 1080P generally.
You will note the Xeon is about 4.4% higher than the Core2 Q9550.
Either CPU when paired with that GPU will likley perform adequately as long as you don't expect miracles. Depending on the game, there might be a slight CPU bottleneck, but not by much - as the GPU proposed is not that strong in the first place.
I would go for the E5450 which is basically a Q9650 - the most powerful you can get for that motherboard as it doesn't support Core2 Extreme.
My old system with a Q9650 (the same as a Xeon E5450) played most titles okay, but it struggled with frame-drops on the likes of Battlefield 4 and Battlefront but fine with racing games. I overclocked from 3.0GHz to ~4.3GHz. After that it was fine at 1080P, with some settings turned down depending on the game. But my GPU was a bit more powerful than what you propose.
You are therefore looking at ~30 fps I guess in most modern games. So consider the r7 260x as a bare minimum for 1080P and be prepared to turn down those graphics settings and maybe OC everything (CPU and GPU) if you want more playable framerates than that.