At that time of day, total time should be less than one hour for both immigration and luggage. Drive into city at that time should also be about one hour, so expect to get in 6-7 am to Seoul. Depends on which stop your hotel is on that particular bus - should run W10,000 unless they raise prices recently.

Bus is the way most people go, very convenient, efficient, safe and comfortable. You can also take bus to city terminal and then catch a taxi.

Either way, way cheaper than either hotel car or airport taxi - deluxe will run $70-80,000, the smaller ones maybe $50,000.