Another thought: if you are going to ski a lot, then buy all the gear. I bought some Salomon Pocket Rockets about 8 years ago when they first came out. My instructor friend lent me his and I fell in love with them (and still am)... but that's another story.
Anyway, they cost a lot at the time, but given that in the 8 seasons since I've not had to hire any equipment, they've paid for themselves several times over.
The other related thought is that I've been told that buying skis is much cheaper in the US (I've not checked myself, so cannot vouch for it). If you do decide to move, and you do have lots of room in that container, you may wish to think about doing some comparative prices research and buying in the US before coming over.
For A-to-A hiking a car can be useful - as bus schedules can be "relaxed" at weekends (especially Sundays) - with services once an hour.
For A-to-B you'll need a party with 2 cars OR use public transport. For those sort of hikes I advise departing from the poorest connected point - and finishing at the best connected.
Oh I second that. Learnt the hard way a couple of times. Waiting for a busy tiny cablecar, then just missing the hourly Postbus to the nearest train station. Adding a couple of hours between hike finish and getting on the train, joy.
Forget the question about bringing over a motorcycle - I have the official paperwork about the move today and it basically forbids putting any vehicle, including motorcycles, in the storage. Plenty of room for ski gear though. I don't know about US v Swiss price for ski gear but even here in US the prices are outrageous unless you wait for sales and get last years model (there is no way I can justify $1200 for a pair of skis.. but $400 for last years model on sale is another story).