Luggage on Swiss Trains

Basically the same arrangements as railway companies in other countries in Europe. All luggage is your responsibility, you have to get your luggage on and off the train yourself, and stow it on board in the same coach as you are travelling in. There are overhead racks above the seat, "A" shaped spaces between the backs of seats, and on some long distance trains only extra racks at the end or in the middle of the coach.
Theft is not a problem, I have never heard of it, but I would not leave your luggage unattended while you go to the buffet car, but if you are a solo traveller, you could ask someone to watch it while you are away.

1st class has the same luggage space as 2nd class, but fewer passengers per coach (2+1 seating instead of 2+2), so slightly more space per passenger. But I would not pay 50% extra for first class, plenty of room in 2nd.

See here for more info including photos: http://www.seat61.com/luggage-on-european-trains.htm

You can use this handy retractable lock to secure your bags:
http://tinyurl.com/m9bqg4n

A number of different types of trains serve Switzerland. This link identifies the types of trains showing on their schedule: https://www.sbb.ch/en/timetable/timetable-information/explanation-of-symbols.html

We rode InterRegio 2nd class to Luzern from Zurich Airport. The car was a double decker with no luggage compartment but a space for bikes. The overhead rack was more for coats and not deep enough for RS carry-on sized bags. I put our checked duffle bag and ski box in the bike space and kept and eye on the bags at stops. Car was only partially full so everyone seemed to just use seat space for their luggage.

Journey from Luzern to Klosters took three trains, an InterRegio back towards Zurich then two RegioExpresses to Klosters. The RE 2nd class cars similarly did not have luggage areas and small overhead racks. Again, folks used seat space and we stored duffle bags and ski boxes near the WC bike area.

The Bernina Express panoramic cars had small luggage shelves at the end of the car but no overhead racks to obscure the panorama view The Bernina Express was a seat reservation car filled close to capacity. One woman had an extra seat and used it for her small dog.

Locking bags to luggage racks in trains is controversial. It would only work on the racks for big bags (which not all coaches have), not in the A-space between the back of seats nor in many overhead racks, nowhere to loop the lock through.
And it can annoy people if your locked bag prevents access to their bag when they want to get off before you.
Never leave bags in the aisle.

And just common sense things like putting your little bags up on the rack and leaving the ground space in the luggage area for big bulky/heavy bags is the nice thing to do.

If one of your travel days with luggage includes several train connections (which do go quite smoothly in Switzerland), you might consider it worth the price to check bags through to your destination station: http://www.sbb.ch/en/station-services/services/luggage-and-flight-luggage/express-luggage.html.

The SBB Online Timetable includes information as to the likely occupancy of the selected train. If you have luggage, you may want to avoid trains with "Very high occupancy expected".

Thanks so much for you comments and assistance.....it has been really helpful :)