The best way to get to the hotel from the international airport is by common taxi, they are yellow. The white is the special taxi, about 50% dearer. Just give them the hotel address in portuguese!
It will cost you 40-50 brazilian reais, about 20-25 us dollars.
You can always ask for assistance at the hotel reception on your arrival.
The hotel does not operate a shuttle service from/to the airport.

Have a nice trip, and dont forget to ask for your welcome drink at the bar!