Can stone ground rye be used to start a starter, or would you need to use medium rye flour?
I have successfully started sourdough starters with stone ground rye flour.
Stone-ground rye works just fine, maybe even better than a medium rye. It has the entire rye kernel, which would lead me to expect that any wild yeasts that may have been on the outer surface of the kernel are still in the mix. No science there, just speculation.
How much liquid would you use for the rye starter?
by weight, then dribble in additional water until the consistency was a soft paste. Not so stiff as the old-fashioned library paste but not so loose as a batter, either.
Understand that there is a continuum of hydration levels that will produce useful results, not a single perfect hydration. What I've just told you is my preference. Drier or wetter starters will still work fine. You can read a blog entry from a few years ago using Tom Jaine's method for beginning a starter. Note that his is based on wheat flour, rather than rye flour, but it illustrates a method at the drier end of the spectrum.
Thanks for your input!