Check in the luggage in BKK and Swiss will load it on connecting the flight booked.
Railway station is within the aiport, trains leave for Zurich main station every 7 minutes, ride is approx 10 mins, trains run like a Swiss clock, Zurich main is right in the city center. You can buy a ticket which in addition to the return train ride includes free rides on all trams, buses and even the boats for the whole day ( Kombiticket). If the weather is nice, having lunch on the boat might be a great experience. Public transport is clean, safe and on time.
Left off the railway station is the Swiss National museum, should the weather prevent you from strolling through the old town.