There's lots of things to consider for a video editing machine, and the program you're using isn't everything, there's also what you're editing. For example, you'll benefit from a more powerful GPU for playback and rendering of high resolution files, and more ram for larger video files. That said, I have a Dell XPS 8700 with an i7-4790 processor for editing short films and some vfx and animation, and it runs fantastic, and it's only a $700 computer.
When looking at specs you'll want at least a quad-core i7 processor, at least 8GB of ram, and some kind of dedicated graphics if only something like a GT 720.
When looking at a processor, go for more cores over a faster clock. An Intel Xeon might he a good choice at the more expensive end.
RAM is easy to upgrade, so I'd start with 8GB and add more if you find yourself running out. I personally never have suffered with 8GB. Clock on the ram doesn't matter that much, just get the cheapest stuff you can.
For the GPU you want an Nvidia GPU. More CUDA cores is what you want. Baseline you've got a GT 720 or 730. A little more and you've got a GTX 750ti. Want to be the fancy kid on the block, get a GTX 960. If you really want to show off, get a GTX Titan X.