Well, if you want 3 monitors, are you thinking, one for gaming and then 2 for misc~ because that's possible, get a gaming monitor (144hz recommended) that'll set you back 220, then 2 additional monitors are pretty cheap maybe 80 each so thats 160, If you want more than 3 monitors you'll have to invest in multiple graphics cards, and if you want a multiple monitor gaming setup you'll need additional graphics card.
With a 1080 you should be able to plug in your main monitor to the displayport slot and the 2 other's to the DVI slots
I would recommend getting an i7-6800k ( or a 6900 if you really want to use money) since you are in the price range anyway
Don't cheap out on the motherboard, a good one will set you back 200 ish
Gotta get an SSD 120gb if you only want essentials and OS, 240-480 if you also want games on it
1-3TB HDD for storage
Gotta get a high quality power supply, you can figure out which range you need by using a power supply calculator.
a good case which can fit everything
Aftermarket coolers for case / CPU also important, if you want lower temperatures and less noise
I'm sure some of the more tech geeks than I will be able to help you out a little bit more, but hey, every little helps. right?