@Chandler Rehbein, a few thoughts:
1. Covering the market: Independent agents sell policies for many companies, but not for the big companies that have built their own networks of "captive" agents. As a result, to shop effectively you have to contact at least one independent agent and then individual agents for State Farm, Farmers, Allstate and perhaps others.
2. Dwelling limit: Insurers vary quite a bit in the amount of coverage offered to replace the building in the event of a total loss. Mysteriously, they say they consult industry databases to determine construction costs, but then they don't come close to agreeing. An important factor is the building information the insurers maintain about homes. Unless you ask to see the information and get an agent to correct errors, the price quoted may be for hardwood floors when you have carpet, a fireplace that you don't have, an extra bathroom, etc. You don't want to insure too little or too much just because the data about your house is wrong.
3. Liability: @Aaron Porter is right about umbrella policies. Check smaller carriers such as Stillwater.
4. Deductibles: Premiums and deductible amounts have an inverse relationship. Consider accepting a higher deductible than an agent suggests, because your premium will be lower. Think about whether, for example, it's worth $100 in premium savings to risk $4,000 more expense if you have a claim. Take the higher deductible if the premium savings is a lot and you think a claim is unlikely. On the other hand, if the premium savings is small and you would be hard-pressed to pay the extra expense in the event of a loss, then you want the lower deductible at the expense of the slightly higher premium. When comparing companies, be sure you have quotes for nearly identical coverage and deductibles.
5. Endorsements: These are extra features that may be added to a basic policy. You probably want to insure for replacement cost rather than what the insurance company determines is the depreciated value of your home or a component, such as a roof. A related feature is called "extra replacement cost" or something similar. It provides extra coverage if the price of labor and materials goes up substantially, perhaps after a natural disaster. The list of endorsements is long. It includes such things as extra costs if a local building code (sometimes referred to as "ordinance or law") requires a rebuilt home to have a feature not present in the home that was destroyed. Another endorsement is "water backup," covering damage from water that flows backward from a sewer system into your home. For each of these, consider the realistic chance of a loss. If the water backup is likely to be in an unfinished basement, your risk, and your need for the endoresment, is less than it is if the water would back up into the main living area of a home without a basement or crawl space. In quotes from competing companies, try to get the same endorsements.
6. Personal property: In an unfurnished rental, you may have very little property that is not part of the real estate -- maybe just a refrigerator, washer and dryer. Companies often quote higher limits than your personal property requires, so you have save a bit by asking the agent for less coverage.
7. Payment schedule: It's almost always cheaper to buy a policy with a single payment. Watch for extra fees associated with monthly or other smaller, periodic payments.
8. Policy scope: Look for an "open perils" policy, which covers losses except those specifically excluded, rather than a "named perils" policy, which covers only the losses mentioned in the policy.