As you mentioned, there are three important components; ram, CPU, and GPU. Another component worth considering is the hard drive.
RAM isn't incredibly important unless you intend to be doing intense visual effects. In my opinion, 8 gigs is the sweet spot for cost right now. If you want to do effects with something like After Effects, Smoke, or Nuke, 16 gigs is the sweet spot. Video editing is largely a linear task so ram isn't as important as in other high performance tasks.
The CPU is very important, but the requirements are very different from something like gaming. Video rendering uses essentially as many cores are available, so an 8 core i7 with a low clock speed would outperform a super speedy dual-core i5. I would recommend either a quad or octo-core Core i7 or, if you have the budget, a Xeon.
The GPU is by far the most critical component, but only if your software can take advantage of it. I always recommend Nvidia because most professional programs use CUDA which is exclusive to Nvidia GPUs. Usually your best option is a GeForce GTX, I would recommend the 660 or 760. At a higher price range you have something like the Titan Z or the GTX 970. Quadros aren't worth the cost for personal use because reliability and uptime isn't a major issue.
In addition to the three previously mentioned components, I would also recommend a 512 gig Intel SSD. They will significantly increase the speed of your computer, especially when rendering. I have seen dozens of articles listing SSDs as the most cost-effective upgrade for a computer.
Another thing worth mentioning is that if you're looking to buy a machine out of the box, look for something marketed as a workstation. Those will have the specs that you need. The personal favorite manufacturers are Dell, HP, or Apple.