To open a bank account for non Swiss Resident, at least in the Zurich area, you can open an account for a minimum of 25,000 CHF but you will have to come down to Zurich to do that. Most of the private banks will not open an account for you unless you have a minimum of 250,000CHF.

My advise is to come over to Zurich and check out the banks. It is easier to do business with people face to face than over the telephone. Due to money laundering laws, the source of your money will need to be verifeid by the banks and how you intend to fund the account.