Follow cipher00's advice about getting replacement value coverage, not actual value coverage, otherwise you'll have to pay the difference between depreciated and new to replace your lost items plus whatever other costs you incur due to your loss. Also check carefully the events covered that result in your loss, especially when it comes to water damage. For example, some do not cover losses incurred due to water damage from a leaking or burst water heater in the apartment. The policy should cover loss from fire, theft, and water damage to cover you adequately.
Also, check with your landlord to see if they have coverage. Some have coverage to reimburse tenants for some losses when they are the management's fault, though they tend to be minimal.
Some people on here suggested getting renter's insurance from State Farm because of already having auto insurance through them. I've had State Farm auto insurance for several years, but when I talked to them around two years ago about getting renter's insurance through them, they said that they could not write any new policies for it. It's a state by state thing though.
I have my renter's insurance through Nationwide. It's a good policy and relatively inexpensive. As someone else said, for expensive single items you may want to get a separate policy. I have a separate policy for my camera, lenses, etc. through State Farm. That way they're covered from loss whether it's at home, in the car, etc.