Here's my understanding about insurance based on my personal experience with rental properties:
1) You'd want a Landlord policy, not Homeowner. The biggest difference is the amount of personal property coverage you want to purchase. Tenants will typically need to purchase their own renter's insurance policies to cover their personal properties. You'll probably buy another renter's policy cover the gap for yourself if needed. Other things that come with a Landlord policy are Liability (also available for Homeowner's), Vandalism, Theft, Lost Rent coverages, though these are mostly optional. Landlord policies are usually a tad cheaper than Homeowner because of the reduced personal property coverage afore-mentioned.
2) Your rates will depend on your own credit score, age, and condition of the property. And sometimes whether you bundle policies with a carrier or not.
3) I personally use Allstate because I have all Homeowner, Auto, Umbrella and Landlord policies with them. So far, they give me the best premiums for the coverages (knocking on wood...). I haven't been able to find a better deal, even from independent insurance brokers. I know they're not the best, but they're the best I could find at the moment.
Hope that helps,
Angie