Most standard homeowners insurance policies exclude liability coverage for aircraft, but will include coverage for “model or hobby aircraft,” like your personal drone. If your policy does offer this coverage, and if you crash your drone and cause bodily injury or property damage, it should be covered by the terms and limits of your policy.
If you crash your drone, it also should be covered under the personal property portions of your homeowners coverage. However, the deductible for your property coverage may be more than you paid for your drone.
Commercial or business use of your drone is not normally covered under a homeowners policy.
If you end up buying a more expensive drone, you should ask your insurer if there is a rider you could buy to make sure it is fully covered if damaged.