IIn the past I've used
RealVNC which will pair nicely with android-vnc-viewer. However, you'll need to know a bit about configuring your router to allow the appropriate ports to pass through to the right PC, make sure it's secured, and all sorts of other things if you want to access it outside of your home network (and please secure your WiFi before doing it, otherwise you'll open yourself up to anyone outside your house having the ability to use your PC whenever you want). Personally I only use VNC over an SSH tunnel since the passwords are passed in plaintext, but setting up an SSH server on Windows isn't something I'd recommend to most.
What may be easier for you is to explore services like
LogMeIn or
PhoneMyPC. Yes, they're paid apps, but if you're uncertain about the issues I mentioned above then they can save you a lot more in the long run thanks to added security.