Generally speaking, no special mortgage is required to rent a property to a tenant rather than living in the home yourself; as long as the mortgage is paid on time each month, you should not have any difficulties with your mortgage lender.
It would not hurt to contact your bank to make sure that your mortgage does not contain a clause that prohibits you from renting your property to someone else. However, I suggest you ask the question hypothetically because if the contract on your loan stipulates that you are the owner-occupier of the residence, and you state to the bank that you are altering the deal to make the property a rental, the bank may demand you refinance.
Unless your loan is through the FHA, VA, or similar mortgage assistance program, your bank likely has no legal grounds to object to your offering the property to rent.
As for establishing a lease with an option to purchase, often called "rent-to-own" or a "lease option," you and your tenant can establish the necessary contractual terms as part of the regular lease agreement. Under this type of lease, the tenant would pay a small percentage of the home purchase price up front, usually in lieu of a security deposit and to be applied to the agreed-upon final purchase price; each month thereafter, he or she would pay fair market rent plus an agreed upon additional amount each month, with the additional payment also applied to purchase price.
To my knowledge most states do not treat lease options any differently than standard lease contracts, so I do not expect that you will have any difficulty in negotiating and enforcing a lease with a purchase option. However, state laws vary widely in the area of landlord-tenant contracts, so I encourage you to consult with an attorney in your area who has experience in contract law before moving forward with a lease option agreement. You will likely want to have a lawyer draw up the lease option contract so you can be sure that all of the terms are legally sound.
I hope this information helps you Find. Learn & Save.