I have had the same problem with people giving little to no notice and not paying their last month. I did require a security deposit for new tenants (ones I didn’t inherit). I think lately with the rental situation in my area they don’t really know 30 days ahead when they will move, when they can get a rental they just go with it. So I am making the deposit equal to a month’s rent now. (I had it lower as I figured that limited my audience).
However, I have not added Last month rent to the upfront requirement. I would limit my audience quite a bit. Most of the people that live in the city for a while are just in shock how much the rents are going up so for me to ask 1st and last plus a security deposit they would be beside themselves (I think).
The owner before me used a non-refundable move in fee. But then the tenant has no incentive to keep the place nice and after putting so much into repairing these (sad) homes I really want to maximize my chances of the tenant keeping it nice. (I only have park owned homes)