When you arrive in Switzerland and registre with the Geminde, you will receive a letter shortly thereafter asking you to tick with insurer you go with. This being Switzerland I am sure you have received it
So it looks like CHF 250 per month, which is about right. This will vary depending on your age, gender, place of residence etc.
Whether you can claim it back from your company, depends on your contract with them. Some companies contribute to health insurance, but this is often for the private one - the one on top of the compulsary one.