buying the components that will give you the most bang for your buck, without stepping over the line of diminishing returns will only set you back about $2300 including a good case, beefy and fast SSD's and a solid 24" monitor. Add another 2 monitors (for a total of 3) and you only add roughly $550 more, coming close to your minimum line. Spending more will only benefit if you want to include a 7.1 audio system with good sounding floor-standing speakers, which I'm sure you're aware, can cost upwards of your entire budget.
IMO putting together a parts list now is a waste of time because new products, especially processor and GPU's will be coming out before your purchase time. Read around and familiarize yourself with the articles here on Tom's and when time comes to put your parts list together, you'll be well informed of what's available and what the potentials are.