Agree with Reeka.. Talk to your HR people first.. Most big companies will have a scheme for this.. Like for me, my company put the deposit amount into a bank account and provided an attestation letter to say it's there.. For probably all rentals compainies, this is sufficient, often no money actually changes hands.
On the permits thing, yeah you should be on a B permit, assuming you're a UK national? Your company should be taking care of the application for that? You do not need to physically have it in your hand for the reantal agreement, again an attestation letter from your company to say it's applied for should suffice (did for me).
You need to make a 'dossier' that all rentals companies will ask for when you show interest in any house/appartment. It should contain copies of passport, work contract, permit or attestation letter, any references from previous rentals, possibly a certificate from the office de poursuite to say you are not being chased for debt.. Maybe more stuff, there's info on sites such as homegate.ch
Once you have all that, then start looking for a place and be prapared for brick walls, knock backs, frustration and hopefully some good luck :) Once you think you found your place, probably another dozen people think they found it too!! So the landlord looks at all the dossiers and chooses a tenant by some magical process. If that's you and you get a copy of the lease, now you can sort out your deposit with swisscaution / employer/escrow -- NOT cash or wire transfer or anything like that.. That's a scam!
It's not always difficult but just be prepared.. I found my place in a few days, zero problems.