The rental you inquired about is an annual rental. There are others. We show 14 annual rentals under $1300/mo between Bradley Beach and Brielle.
I am the rental manager in my office and can help. I have others that are not on the MLS as well, including a 2 bedroom in Avon for $1600/mo.
As far as insurance goes, Met Life has a reasonable policy.
If you would like help finding your next home, reach out to me via Trulia or my website, below.