Look at the new Mac Pros for this work and get the best configuration you can afford.
With a budget up to $4000, you should be able to purchase a nice Mac Pro system for your needs.
Does this price include the purchase of software OR is software another added part of the budget.
If this includes software, then I suggest, but not necessarily recommend, the top of the line 27 inch iMac.
Purchase this 27 inch iMac with the fastest, optional i7 CPU, optional 4 GB VRAM GPU and just the base 8 GB of RAM.
RAM is user installable in the 27 inch screen model iMacs and you can get RAM cheaper from other third party source than from Apple. I am not keen about the new Fusion drive technology in the new iMacs, so I would opt for a standard large capacity internal hard drive and maybe add a third party, externally connected (USB 3.0 or Thunderbolt) high capacity SSD drive, instead.
Also, purchase a large capacity hard drive for backup storage.
Forgot to add, budget for 3 year AppleCare.
And if you are going to do a lot of film work on this computer, ditch the wireless peripherals (big battery wasters and can be unreliable) and look at the various Mac compatible wired keyboards and mice available to use with your new Mac.
If you plan on using Apple's Final Cut Pro X (and I advise you should be) there is a keyboard company that makes a custom keyboard just for using with FCPX.