Dealing with existing tenant with no lease. (New York)

[Nick Carlson]

I just purchased a property that has a tenant in it who has no lease, is month to month, with no security deposit. As tomorrow is the 1st and nothing formal has been set up I was planning on collecting the first payment in person, as I assume the previous landlord did, and then move to an online system afterwards.

As the tenant is currently paying about 200/month under current rates (600 vs 800), i'd like to either raise it up slightly (700~), or remove the tenant after 90 days and do some renovations and then rent out for market rate. How do I properly approach this situation? Is this a situation where I give them an ultimatum of either the rent goes up in 90 days or here's your 90 day notice and provide paperwork for each situation? 

Even before that, would I provide them with a lease agreement tomorrow, requiring a security deposit, that would be month-to-month for the interim?