$1k is a bit tight to build a comp for this game. If your current rig is still in decent shape, could you ask your builder to re-use a few parts – the case, power supply and optical drive perhaps (if its SATA)? This might save around $200. That would allow you to focus on upgrading your MB, CPU, GPU and HDD (or SSD). Something like this:
i5 4670 CPU – $236
Asus Z87-K 1150 Motherboard – $141 (get correct form factor, depending on case)
Samsung 256G 540/520 SSD – $255 (solid state drives are worth every penny)
8G 1866 RAM – $84 (looks like your builder carries Crucial)
EVGA 760GTX Video Card – $289
Total – $1005
A CPU cooler is a smart investment at around $40. Maybe your builder will hook you up for being a good customer? If not, dip into the beer fund and buy one anyway. You might also be able to re-format and re-use your current HDD for extra storage.