Re: Inherited Winchester 62
That rifle was made in 1947, along with 35,329 others; total production was some 409,000 between 1932 and 1958.
There is collector interest in any Winchester, but there were so many of those made that they bring serious money only if like-new in the box. That rifle has been well used, and probably gave your father many moments of pleasure, but it shows the use. In dollar terms, it would sell, retail, for around $300. As a memento of your father, it is priceless.
I don't know the terms of your insurance policy, but generally a few guns of moderate value are considered part of your personal property and covered automatically. Whether to pay an extra premium for that gun would be your decision.