divine,
you need to check if your video editing software is gpu accelerated or not. in many cases they are not and are mostly cpu driven where a gpu only serves to make playback less choppy. if however it is gpu accelerated then you could benefit from a better card.
the build below assumes you do not need a gpu for playback so i only have a low end one included for non-choppy performance. it is 4k capable.
i have 16gb of ram in case you were encoding 4k video. otherwise you might be able to make do fine with 8gb.
i also have 2 hard drives since when encoding from one drive to another drive (source and destination) times are going to be less.
the power supply is overkill but with MIR its a good buy at the moment. otherwise any unit from xfx or seasonic around the 500w range is fine (even less is needed but i didnt do a calc to see just how low so this is a safe off the top of the head number).
http://pcpartpicker.com/p/tBRh23 its just a touch over your budget.
if you benefit from gpu acceleration then i'd drop the one hard drive and bump up the gpu to something better.
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actually... the xeon based build listed by anton would also work very well, perhaps with a bit of modification. perhaps bump up the ram, go with a cheaper case and bump down the gpu and it works good.
the xeons are basically the same thing as the i7s but without integrated graphics which means less money for the same thing. if you are already using a graphics card then it doesnt really matter if you are missing this or not. your call of course.