My husband & I have been fostering for several years & for the last year we have worked with our local animal shelter. Rather than ask 'what's the most important question to ask about the animal', I think it's really important to visit with the animal & make sure that they are both comfortable with you & that you are with them (all members of the family, if possible). That said, it helps to describe your lifestyle, to ask the following:
Where have they seen a vet?
How old were they when they came into your home/rescue/shelter?
What food & supplements have they been on?
Have they had any medical/surgical/behavioral issues?
What animals/humans/ages has this animal been exposed to?
Developmentally, what can I expect (behavior/attitude/growth)?
What will this animal need (house/yard/exercise/fence/space)?
What have they been tested for?
When should they get their shots/exams/check-ups?
When I write the bios for our kittens we try to answer as many of those questions as possible & describe (as much as possible) their personality. We also try to welcome the potential adopters into our house to visit with the babies - sit on the floor with them & play or hold or just watch their level of activity. I have, as much as possible, encouraged all the folks who want to come over to do so. We have loved working with the adopters & the kittens!
Oh, one more thing - you may want to ask if you can have someone's phone number in case you have any questions... I often get phone calls from 'new' Moms & Dads with questions, like: 'Is this normal? Should he/she do this? What about this? Should I worry about this?', etc... It's completely normal & there is NO BAD QUESTION! (You can always ask here, too)... Good luck & have fun - but don't look for a certain animal, let them choose you - you will know when you meet the right one!
#AdoptingaPet