I would take the train into the city upon landing. The Local VY trains are much cheaper than the airport express and only a few minutes longer.
Search for Oslo lufthavn (Gardermoen) to Oslo S
https://www.vy.no/en
Plenty of hotels around Oslo Central Station. Pick from Thon, Scandic, Radisson Blu, Clarion. If you're just looking for a convenient place to sleep any will do, if you're looking for specific amenities, choose accordingly.