Responding to a prof's email about acceptance in a PhD program
I'm at an R1 and have been sending those happy informal e-mails to students ahead of the formal notification from the graduate school. And I've been corresponding with a few who have responded.

My expectations are that you should be thrilled but I also think you should hold your cards close to your vest, just in case. For example, maybe your 'B' school offers you a much better financial package. In that case, you can ask us if we can match. And even if you don't have a competing offer, you have leverage while you haven't made a decision.

You could also ask if there is a campus visit day for prospective students. We plan ours in mid-March and it's a good way to meet other grad students and your future advisor. You might be able to get some travel funding to attend.

If you're going to say no, you should say no as soon as possible, as you might open up a slot in the waiting list for another student. But if you're thinking about saying yes, then there is no disadvantage and considerable good reason to delay saying yes until near the deadline. Advisors not only know this - but if they are good advisors, would advise you to do this.