So I've got mediacenter running on a headless linux VM that isn't used for playback at all, just as a server (for similar reasons). It runs on debian with xfce4 installed.
MC itself is using about 4G of ram right now, but almost all of that is cached/buffered memory that MC will yield back if asked (i.e. optional, not necessary). The current "hard" RAM usage for MC on my system is about 200MB of memory, but that increases during transcoding which may or may not be in the mix for your setup. I've run this VM with 4G total RAM and it worked just fine, but performance suffered a bit. Obviously MC can run on older raspberry pis that only have 1G RAM total, so it's absolute "needs" are relatively small. I'm currently running at 8G RAM, and that seems to be plenty for my uses (mostly as a library server, but some TV recording and light transcoding).
I can't say how much RAM you'd need in a windows VM, but thought this might be a useful data point.