if so, then i would suggest using in i3-2120(i5-2500k would be out of budget) along with a good z68 mobo.(a flashed bios z68 mobo is compatible with gen 1 ivy bridge processors if you ever want to upgrade, only difference between a z68 mobo and a z77 is 77 has innate ivy bridge support, built on usb 3.0 and a few other experimental kinks). A good z68 mobo would allow you to decently have a good range of room to upgrade your processor if you need to in the future.
OR
spend rest on upgrading that mobo and/or gpu
There are pros and cons of deciding between an i3-2120 and a 965 be
965 be Pros: Can be overclocked, Quad Core, Does video benchmarks better(i.e video encoding), certain games that utilize all core threads will run better on the 965 be than the i3-2120
i3-2120 pros: lower power consumption, sandy bridge architecture tends to do better in gaming in general. z68 mobo choice is a solid pick. Lower temperature.
Both have just about the same amount of power