Our Family had our first visit last year. We got the button when we checked in. But other than that we did not get any special treatment at the resort.
At Crystal Palace Tigger gave my children a lot of attention he must of stayed at our table for 20 minutes or more than came back and got my 7 year old dd to lead the parade with him. I don't know if this had anything to do with us wearing our First Time Visit Buttons or not. We also ate at Chef Mickey's, O'Hana's, San Angel Inn, Holly Wood and Vine, Garden Grill, CRT, and The Whispering Cayon Cafe. All the characters were really attentive at the Garden Grill but again I don't know if the button had anything to do with that. As for the other restaurants we didn't receive any special treatment and the servers or CM's didn't even comment on it being our first visit.
When my dd wanted to see the Fairies there was an over 50 minute wait and we had dinner reservations, I asked the CM if there was a place where she could just look at them from a far without meeting them, she said no. I said ok, as we were turning to leave she was on her phone then she called to me to wait and gave my dd a pass to go back stage ahead of the line and meet the Fairies. Again I do not know if this was because of the buttons or just Disney Magic.
Also on the bus our last night we were standing at the front of the bus and th bus driver announced over the PA system for everyone to give us a welcome because it was our first visit. This really made my kids feel special.
Wishing you some Disney Magic for your first trip!