As long as you avoid taking the S Bahn service from ZRH to Zürich HB (changing there to a service to Geneva) which uses Stadler KISS or Siemens Class 514 double-decker EMUs (where you'd possible have to haul your carryons up the stairs where there's not too much space to stow it), you should be fine regarding your baggage.
The airport railway station is connected to the terminal, but it's quite a trek to get there, as the station is across the road from the terminal. Upon arrival, follow the signage towards the station downwards, and after a walk of maybe 5 to 10 minutes, you'll end up at the stairs down to the platforms (near Check-in 3). There are both a ticket office and ticket vending machines right next to the escalators.