Definitely want to reach out to as many kinds of folks as we can!
Mentor availability will be the limiting factor for the first run: In the preliminary poll we were running a bit over 2:1 would-be mentee to mentors, so want to get all kinds of mentors lined up.
I’m not sure of a good way to handle the diversity issue in matchups. From things people have said, I think we’ll have plenty of people who want to step up on that front – but with the numbers imbalance the odds are against us having the ideal matches for everyone who is looking (on either end). My initial idea (in the draft above) was that the mentees would be the ones to state their priorities rather than us using demographics directly (ie – it’s possible that some female TA really wants a female mentor , but equally possible they’d really like somebody with experience in AAA more) so my first pass idea was “say what you want and we’ll try show those (anonymized) preferences to the mentor volunteers and see who thinks they’d click with you”. But we could certainly include demographics too.
Robb’s speed-dating idea approaches the same thing from a different angle, I’d be curious to see what others think cause, honestly, it’s a lot less work 
But I’d worry a little bit about it being too like real dating, ie, the candidates who get picked first will be the self-confident, high affect, extroverts.
The big thing is that we’ll definitely not be able to serve everybody right away, I’m very reluctant to let anybody take on more than one person for their first time (I do this sort of stuff for a living and 2-4 is a lot of people to really try to get involved with even if you do it all the time!) I’m open to any proposals about how to do it well – my hope would be that a year from now we have enough momentum and community experience that the wait times and quality of matches get better as people get used to the idea.
As for sign ups – the form it takes will depend on the outcome of these conversations; this is a good time to suggest practicalities!