There are pros and cons. A lease locks in the rate for the term of the lease and affords the tenant some protection. No lease gives the tenant more freedom, but no protection in terms of the rate or stability. Make sure you get a month-to-month agreement.
You should always have a lease agreement reduced to writing to ensure that your interests as the lessee are protected. Without a written contract, you will be unable to take the property lessor to court to address any grievance or controversy arising from your tenancy. A responsible property owner will always insist on a written lease agreement.
It is never safe anywhere to do a rental without a signed lease. The terms will dictate the rate and term as well as the responsibilities of each party. Without that it deteriorates into a "he said - she said" dispute. The process from there would probably be litigation and a lot of expense.