By favorite fursona, do we mean "overall", "Personal", or that of another person?
My reaction to all of these would be the same: study and take notes. Just the fact of seeing a real life furry (and not a person in a suit) would stun me while the subconscious part of my mind takes control and demands to know Why, How, and What. Once I fail to come to a logical conclusion. I'd probably try to follow them without being noticed.
If we're talking personal fursonas, It'd be very awkward. Otebon is me with a few fixes (mostly physical), so it would be a chance for me to see what I'm actually like.