$3000 will get you pretty much anything you want, and you could even work in a titan in there too with enough planning/ deal scouting especially since you are ultimately looking to complete/ execute this project in September-October.
What kind of gaming machine are you looking to build?Are you using the build for gaming only, or are you looking to video edit/ data crunch? I ask because if you are just gaming and use the computer for personal normal workstuff then you should start with the core i5 and start your build from there. The only real difference between the i5 and the i7 is the hyperthreading and to my knowledge games don't use hyperthreading and the 1-2 fps (if any) you gain from the i7 is from it's naturally higher clock rate.
As far as monitors are concerned, I us a 32" Samsung TV that I got on super sale and I love it, and I use a second 24" mid range monitor for normal computer stuff. But for $3k you might be able to set up three monitors if you are into that setup.
So again think about the build you want and the forums will be more than happy to bounce some ideas off you, but with enough forethought/ deal hunting you could most like get everything you want for $3k.