Yes, you can put your parts on a receiver if you mean that by "build" but you'll need the tooling and it's not at all as easy or the same thing as putting together an AR15 (just so you know what you're getting into).
It sounds maybe the Siaga route might be overwhelming to someone unfamiliarized with the kalashnikov but it's relatively simple to reconfigure on yourself.
I'd say go the Saiga route. What this is, if you don't know, is actually the high quality Kalashnikov rifle built in the actual Russian factory; However, when it gets imported there's some ignorant laws that require the rifle to not have it's intended configuration so allot of people do the gunsmithing themsleves and fix it. While the imported rifle is fine on it's own, IMO you stand to benefit in different ways from "restoring" the rifle.
Used and wholesale parts can be had at way better prices than as advertised by major companies but you have to be resourceful. For the $, the Saiga is the best option. You will pay the same or more for the already mentioned and typically litlle lower quality Century Arms rifle (although my WASR 10/63 is pretty damn awesome).
Most AKs won't have mag issues, you just have to watch for the single-stack or double-stack magazines because the magwells will be different. Also, .223 caliber AKs have a big mag thing I won't get into but basically as an example the Saiga .223 they can take Weigar mags, Orlites, Galils, etc...