Down Payments (security deposit) typically equall the monthly rent. This isnt always the case, but a good rule of thumb for planning purposes.. If there's an animal involved, then the down payment (security deposit) could be slightly more to cover potential animal damage.
I see you are asking about rentals, not sales.............so what you want to know is how much upfront money you need - not a down payment - in my area, a tenant needs the first month rent along w/ a security deposit paid before moving in..................the tenant also pays the commission.
Find a local agent who can give you specific amounts, as they will vary from area to area.
There are non-profit organizations that will gift you the down payment and closing costs to buy your home so it would cost you "zero down payment". If you do not want to go thru a non-profit, you can put down as little as 1% down payment. A house of $160,000/your down payment would be $1600. Please call me and I can share all the details with you. I specialize in niche products for first time home buyers.
My direct number is (925)354-7475