Distaria: Bring up the visitor list, then the buttons along the bottom let you sort them by race. Just de-select all the others exept the grays, then pick one with a good spread of skills, then click on him in the list, then his picture to zoom to him. Right click him(in game) to bring up his info page, then hire him.
EDIT: They don't always say yes, if they shake their head, an icon will show what need he's trying to fulfil. You can't wait, or just try to hire a different one, I usually just move on and get somebody else. A small trick: if the person you want to hire is sleeping, you can be a jerk and beam up the sleeping pod, immediately booting the occupant, whom you can then hire. Kinda mean, but who said you had to be nice?
Thank you for your reply. However, I only have Salt Hogs listed and no other race. The message keeps telling me to hire a Grey for the hospital, so I'm kind of stuck now. I keep watching to see if another race shows up but they don't.