Location and secondly price will be a major dictator to the results of renting your property and your potential income. Island rentals are very attractive for many people who have a boat and have comfort with the tranquility and peacefulness of island living. As an owner, you are undertaking much more challenges in maintenace and transportation of everything from mainland - however well worth every challenge! Generally, you purchase island property for less than mainland and the rentals are less on islands verses mainland property. I have had personal experience and success with handling my own rentals and servicing the rental guests. A great experience however living locally makes that economically feasable compared to living out of state. I regards to your concerns of theft and keys, the quality of rental you provide dictates the quality of your guests. However, I certainly beleive any folks willing and able to pay your rental fee will have no desire or plans to steal from you. If they like your rental and location, they will do as much as possible to please you and have the opportunity to return another season.
If you find a place or have any more quesitons, private message me and I would be glad to offer any help as a local! Lake Winnipesaukee is the only true life to live!