The cost of renter's insurance is pretty much driven by the amount of contents you need to insure. If you have an accurate estimate for the value of all your contents (all your belongings, furniture, clothing, collections, electronics). Some contents may require separate coverage depending on the value of the items. For example, jewelry and fine arts may have limitations on the policy. Jewelry is commonly limited to $2,500 on policies and many other policies may offer less coverage. You may be in need of a collections or jewelry "rider" to accomodate for high valued items or large collections.
Liability is included and the coverage amount can be manipulated if necessary. Companies offer a number of deductible options ranging from $250 to $5000. Normally I advocate taking large deductible on Homeowner's contracts, but for a renter, take a deductible that is on the lower side. $500 to $1000 is a good range. You also may receive discounts for having a doorman, alarm system and/or surveillance cameras.