I would recommend you purchase a renters insurance policy. These policies are relatively inexpensive, but can provide great benefit in a claim situation. The renters insurance will provide insurance for all your personal property up to the limit you purchase. So if there is a fire, you would have coverage to replace your personal items like clothing, furniture, and dishes.
It will also provide personal liability coverage. For instance, if someone is over at your place and trips over an electrical cord and hurts themselves - if they come after and sue you - the insurance company would provide legal counsel and help in a lawsuit up to the limit purchased.