Hestia arrived a lot earlier than probably a lot of people because she's really tired of staying in the safehouse and would have, at some point during the night, begged Professor Dumbledore to let her live at Hogwarts (please please I'll be good, I can help with things from here, etc.). Before and after the meeting, she would've been very social and talkative and friendly and such and would've thanked Elsie for baking the cookies and congratulated Meaghan and Caradoc and so on and so forth. She has cabin fever (it's burning in her brain).
During the meeting, Hestia would've been a lot more participatory than she otherwise would've been, particularly bringing up the newsletter and pamphlets and things like that, which she really wants to help with. She would've talked also about how they can use the info from the listening devices to give more information in the pamphlets/newsletter and wondered aloud if Hogwarts has a printing press somewhere? (she's sure it does) She also would've asked if there are any plans for rescuing Muggleborns (keeping her mother esp. in mind) and their supporters and volunteered to help with that as well.