There are local buses to suburbs close to the airport, not to the city center.
There are no Uber in Germany. Taxi would not be much faster, specially if your destination is very central (traffic in central Frankfurt is poor) and would be much more expensive. Di you have lots of luggage ?
The train is very convenient as there are several stops on the line in the city center. What is your hotel ?

Edit to clarify: The app Uber will work but it will call a regular taxi, not an Uber per se. You are better off getting a taxi from the rank as there is no waiting time.