I would love to own but I rent so I use renters insurance (State Farm). First I needed to buy a renters policy (cost about $250/yr depending on amount of coverage, deductibles, liability ect). Renters insurance only covers personal damage and damage or loss within the house ( fire, theft, flood, ect) and some policies will cover contents of the car if in front of the house. Make sure to ask a lot of questions now so the insurance company can't deny your claim later. For example I live in WA state and earthquakes are not covered in a standard policy and need to be added at an additional cost (something I had to ask). These policies also cover you in case you do something that damages the rented property ( and recently saved my a$$).
From there I added individual riders to cover my camera and computer gear. Riders are cheap ranging from an additional $10 to $25 extra for a whole list of items. Riders are different in that you need to provide a serial number of everything you want to cover and a receipt or a link to a site showing cost. Items under the rider are covered, without a deductible, against pretty much all possible outcomes that are considered "loss" of the equipment , both inside and outside of the home ( theft, accidental breakage, malfunction beyond warranty ect..). Unlike the renters insurance policy, if I drop and break my camera, or its stolen at a shoot, the rider insurance will pay for the replacement.
Each company will have different requirements and prices so it is best to check before you purchase. The best question to ask isn't "what will you cover?" rather "how can you deny my claim?"