Here is my try at it:
http://pcpartpicker.com/p/hUge
It comes to just over 1000EUR, so it is over budget, but I went overboard in some places, and it would certainly be possible to choose to modify the build in certain places. I would personally keep the i7-3770K, because skimping on the CPU is going to make encoding videos extremely painful to wait for.
The graphics card I picked is basically the least I would want to be stuck with myself. I would suggest going for an EVGA GTX 570 or 670 (the 500 series actually benchmarks better than the 600 series for some models, so saving money by choosing a 570 or 580 is a great idea, though the 600 series may offer power savings over the 500s). I don't know anything about AMD/ATI's graphics cards. I always go with NVidia cards because their driver programmers are far better than ATI's programmers were. AMD may have fixed that problem since they bought ATI, but I haven't tried them out since AMD made that purchase, so you would have to ask someone else about AMD's GPUs if you want to go that route.
If he is dealing with videos that large, then I doubt you'll be able to fit a big enough solid state drive within his budget. I would suggest getting a couple of 1TB 7200rpm hard drives, and when it comes to hard drives, Western Digital will give you the best value. They offer a 5-year warranty on their Caviar Black line, and those drives perform really well for spinning disks. If you are planning on upgrading to any serious RAID configuration, then you should trade in the Caviar Black drives for their RE4 drives. The RE4 drives have error correction parameters set that cause them to perform better than normal consumer drives in RAID configurations, and they carry the same 5-year warranty as the Caviar Black series drives.
The case I chose was a random pick from cases that I've seen recently that I thought looked cool. That is all it is. A case is a very personal sort of choice, and I would really just leave that up to you and your friend. A lot of money can be saved right there.
8GB of RAM is basically the new "enough". I, personally, would just start off with 16GB of RAM, but I do stuff like run multiple 4GB virtual machines, so I need a bunch of RAM to do that. 8GB is plenty to handle every game ever made so far, and it is enough to handle most other programs, too. Video editing is helped greatly by adding more memory, though, so he should really be trying to expand to 16GB in the future if he doesn't start out with 16GB now. I would just stick with 1600MHz to save money, and I certainly wouldn't go below 1600MHz. Most LGA 1155 motherboards have 4 DIMM slots, which is why I chose an 8GB kit that has two 4GB DIMMs. That leaves room to upgrade to 16GB later.
Anyway, you can take this and add/subtract to get closer to where you're trying to end up. I hope it helps.