When we first moved here - not speaking a word of German - a relocation company 'took care' of many such things for us before we arrived in Switzerland... a seriously bad move, we came to find out.
The insurance agent gave us an English summary of the policy - but his summary certainly didn't match the official version.
Once I'd had a few German lessons under my belt I realized that we were locked into a 10 year household contents and liability insurance contract that covered all sorts of things we did not need, and didn't cover that which we did. We ended up having to purchase a second policy to cover the things lacking in the first.
Stupid of me, I know - but coming from a system where pretty much everything runs on 1 year contracts, it just didn't occur to me that a contract could run for so long. Live and learn.
(Apparently the relo company automatically signed all expat clients up for a standard 10 year policy because "Well, you'll be transfered to another country soon anyway, and you can break the contract then."

I don't think the firm is still in business.

)
10 years on, once we were free of the old insurer, we switched to Zürich Insurance who not only were substantially cheaper, but also provide a contract in English.
The moral of the story is: Don't sign (or allow a proxy to sign) anything you don't fully understand.
O - and yes, you should definitely have private liability insurance. And if you are renting, make sure you are covered for any damage to your flat - Swiss landlords are very strict, and a few little scratches can turn out to be very expensive. If you have pets, make sure you are also covered for damage they might do.