My daughter had her adenoids removed just before her 2nd Birthday for constant sinus infections, which led to a horrible cough all the time. A few suggestions:
Have them do the tonsils as well. Recovery will be longer but I wish I had demanded they do the tonsils at the same time. If your child needs tubes ask them to do those as well. It is close to a year later and they think she now needs tubes and are talking about tonsils. They even suspect her adenoids are growing back. (happens in about 1% of all cases)
Demand a preventative antibiotic to be taken for ten days after surgery. They did not give me one and my daughters surgery area became infected which lead to 20 days of antibiotic and a very uncomfortable little girl.
In my experience my daughter tolerated the surgery very well. She woke up and asked for a drink. She was a little out of it but did not get scared. She loves her doctor so she was not afraid to leave with him before surgery either. The recovery did not go as well as some claim. Allow a day or two for your little one to rest after the surgery if you do just adenoids. If you do the tonsils give them a week. It is my opinion that it is not fair to anyone to send them to daycare right away.
That is my two cents. Good luck and I hope it show dramatic improvement in your little ones health.