Just throwing out there, there's basically NO difference between an "i3" "i5" and "i7" for gaming except clock speeds. They're ALL dual cores with hyperthreading.
Either buy an i3 and save your money, or buy an i7"QM," which is the only quad core mobile CPU in that lineup.
As for the budget, I don't have time to look for it right now, but for whomever comes next, that's about $1250 usd.