For the CPU, probably intel, and you want at least dual core, with the fastest core speed you can find. The main thread in DF runs single-core, but you can give it more room to run by having dual or quad core, and things like graphics, operating system tasks run in the other cores. Since DF is mainly running in one core, base core speed is very important, as compared to multi-threaded apps where having many slower cores can work better.
A large CPU cache is important too, this is built-in RAM on the CPU which backs up data from memory in the background. It reduces memory wait times because often-accessed memory is backed up on the CPU. So high cache ram is important for cpu-intensive apps.
Fast RAM is very important, so you need to research DDR3 / DDR4 ram and find which ones have the most data throughput. Different motherboards support different speeds. DDR3 is cheaper and supported by more motherboards. It runs at speeds of 800-2400, so you really want to just go straight to 2400 if you get a DDR3 motherboard. DDR4 is new, more expensive, and runs at speeds of 1600-3200, so it would give you more room to upgrade even if you can't get the fastest RAM right away.
You might get a little improvement by running DF off a fast solid state drive too, but mainly for things like Autosave. This is something you can tweak any time though, so you don't need to consider it as part of your build.
Things like video card aren't going to be very important, since DF doesn't tax these systems. A built-in video or a video card pulled from an older machine will be fine, just check that the new motherboard has a compatible video card slot with any older card you want to use.