Settling on a new property with Current tenants

I will be settling on a 3 unit property in another week, where the seller will continue to reside for a few months so they can find their next property. There is an existing tenant that will be living there on a month to month basis. It doesn't seem like the current seller has a written lease with the tenant. The seller is telling me that he used the tenant's security deposit for repairs. 

The steps I am looking to take are: 

From the seller: Get a deposit and a lease for the time I have agreed to allow them to stay. 

For the existing tenant: Request a deposit and a lease for a month to month basis. I am expecting to raise the rent for this apartment. I am thinking of giving the tenant 2 months notice of this increase to allow them to prep for finding a new place if they do not agree with the new price. 

Is this the proper way to go about this? Is there anything that I may be missing?