Moving to Switz in Aug - could use advice on car, banking & more

Hi all- We are a family of 3 from the US moving to, likely, the Ticnio area of Switzerland (right near the Swiss-Italian border). Our 9 year-old son will attend an international school. We have applied for the family reunion long-stay visa as all my husband's aunts, uncles & cousins live in Switzerland & his mother is still a citizen, despite living in the US. He speaks Swiss-German.
In any case, what is the best company to rent a car from, long-term? We looked at Peugot & Citroen via Auto Europe, but they may have some stipulations if you want to reside in Switzerland? Also, I assume we should open up a Swiss bank account so that we can pay for rent, etc. & not have to deal with withdrawing money from an ATM every time & paying a lot of fees.
What about apartments-- I see many that say "3 rooms" -- not bedrooms, but rooms. What does that mean?
Finally, what's the easiest way to ship a big box or crate of our things from the US to Switzerland?
Thank you for any/all advice you can give.

Hi Nicole,
did you change the next destination from Italy to Switzerland (Canton Ticino)?

I guess residence/work permit is all under your control.

Regarding Housing:
Yes, usually ads describe a place with total no. of rooms, considering that a tenant will use the rooms to his liking, e.g. Bedroom(s), Master-BR, Living-Room, Dining (area or even room). If an ad reads; 1.5 baths, it's usually 1 full bath and a guest toilet/powder-room). I am more knowledgeable about Housing and related Relocation in the Basel area, but would consider that rent for housing is more expensive than in the US. At best you get a Lease with legal termination clause which is 3 months, as per each month end, except end of December (by CH Law). You will discover a gross and a net rent, the gross rent = net rent + utilities, such as heating, Water, etc. Electric power usually is directly to be paid by you to the provider, Same applies to Communication provider. Here I suggest check online; SWISSCOM and upc cablecom.
Regarding Banking in Ticino, I suggest you consult Credit Suisse &/or UBS, I know that in Basel US Citizens can open accounts at such banks once they sign all documents related to FATCA.
Other local banks are extremely reluctant to accept US Citizens.
Long term rental commonly is likely leasing of a car. Should you interested in Car Leasing, mind the following; monthly lease rates are taxed (VAT = 7.7%), opt for a Non Downpayment contract, ensure that the Residual Value is more or less realistic after the Lease term, at times you be offered a high RV in order to reduce the monthly rate, also ask for different mileage use, e.g. 15'000; vz 20'000.
As an alternative you may check on MOBILITY car sharing, there you sign up for a membership and pick up a car any time needed at numerous spots.
Of course there is always the option to buy a car in CH, perhaps even in Italy, where you would pay 23%VAT which you could net against the 7.7% Swiss VAT. Custom goes by weight of a car and is rather of small fee. I would not be surprised if you could find car dealers, e.g. in Como delivering car, all documents done, to your doorstep.
As you have not relocated I suggest to obtain an International Drivers License, e.g. through AAA.
The US License can be used during 12 months from the date you enter/register in CH.
Regarding moving items, surely suggest you contact International Forward Movers, as they have the expertise.
Mind you Ticino is not just at the border to Italia, the locals in Ticino speak mainly Italian, which is one of four OFFICIAL languages in CH. This means e.g. all official forms, like a Lease are in Italian.
Last but not least, there is a useful link www.comparis.ch (switchable to English) providing an enormous amount of info, so is www.ch.ch.

All the best.