Welcome to My Swiss Alps -
Many stay at or near the airport. That tends to be a higher cost option, and you still may find it takes 20 minutes to get to the airport if your hotel has a regular shuttle schedule, or, you are not really close to the the terminal ( as in cheaper hotels). I stopped doing that long ago, once I saw how good the public transport system is.
So, take the train. Unless someone else is paying for the ride. In that case, take a taxi. ;-)
No problem with bags...everyone else will be doing it. Most trains have luggage racks in the compartments. The double deckers have large vestibules where people stand with their luggage. That works best if you are among the earlier passengers to board. Since there are frequent trains, that is not a problem.
The timetable will tell you the track number for departure. Tracks #3 - #18 are on the main level and easiest to access.
Higher numbers are at track levels below the main station and require 2-3 extra minutes to get to them. Good signage.
The luggage carts at the station and at the airport go up and down escalators. Don't overload...they do take on steep angle.
At the airport, they are free.
At the main station, they are in a queue, chained together at many places thughout the station and near the entrances.. A 2 CHF coin unlocks (unplugs) the cart. When you are on the platform for your train there are places to plug the cart back in and get your 2 CHF back. Or, you can forget it.
Seems to me that your biggest problem will be getting your bags to the main station. Under similar circumstances, when I could put my business clothes in a suitcase before a few days of leisure at the end of a trip, I'd do so and ship the suitcase to the airport.
The SBB web-site that has the time table explains luggage shipment.
When I have not had the luxury of a couple of days for my luggage to get there from the back country by the cheap option, I stash a bag in a luggage locker at Zürich main station or at the airport, so I don't have to get it to the airport in a rush. Lots of lockers, many large ones, one level down from the main train level at the main station. Good signs.
There is a left luggage office if you need to leave your skis, which won't ft in the lockers. , but it seems that it opens only at 0730. I remember earlier....you can check at the station.
If someone else is paying, take a cab from your downtown hotel. Have them book it the night before. Avoid the Ben Bus Service. Only 25 CHF, but he goes to multiple hotels before he goes to the airport. Can cause you to worry if you have an early flight and are short on time.
When my wife and I traveled together and she did not feel like hauling luggage, we took a taxi. 65CHF. 20 minute or sometimes less. . The heavy traffic is inbound toward the city, not outbound toward the airport.. If feeling lazy, I still do that.
My preferred hotel is one of those that forum recommends - The Hotel Adler. 10 minutes walk to the main station with somewhat less luggage than you have. Or, two stops from the main station plus 70 meters walk on the #4 tram. Trams run every 8 minutes. Most but not all are the newer models with a floor flat at the level of the platform. However some still make you go up a cople of steps to get on board. There is a hotel at Central ( a tram station) 3 minutes walk from the station. It's OK. Full of tour groups.
A friend stayed once a couple of years ago at a basic hotel on the other side of the station, close to the mid-station underground walkway. No food. Starbucks close by. He and his wife were happy with it. Hotel Walhalla. I've never been there.
map.search.ch/?pos=683122,248410&z=25 6&poi_id=a6a62234eff40 b6a-tel&poi=bergbahn,halte stelle,hotel,parking,v iasuisse,zug
At the hour of the day that you are traveling, there will be approximately 8 trains per hour from Zürich main station to the airport.
I have attached a screen grab to give you a sampling. Avoid the #10 tram. It takes forever, but, is the cheapest option.
Please check this instruction page:
then look up the trains departing Zürich Hbf (Hauptbahhof, main station) for Zürich airport (Flughafen) on your date and time. You'll see trips as short as 9 mutes and as long a s 20 minutes...with stops.
I've not used Uber in Zürich.