How much should the form remember? Which fields are considered safe?

I was creating a site, that has a product page with a small three-field form:

  • name
  • email
  • phone

To send the form, user shouldn’t be registered.

They say, it’s better to start with something, so my first intention was to make form to remember all entered fields (even if the user hasn’t submitted the form – she won’t need to type if she decides to send it later).

Then I understood that on public computer it can expose some personal info to another person, like phone.

So is it a bad idea in general to save fields in the forms? Are there any fields that are “safe” to save? Or is it better not to save any fields, but leverage autocomplete feature?