Moving from Manhattan to Brooklyn. ALONE. Advice?

I am currently living in Manhattan with 2 roommates. I plan on moving out sometime soon before school starts at the end of August. I will be living alone. Our lease here is up August 31st, and I don’t want to break it.
I realize that rents get more expensive in the summer. I am looking for a studio or one bedroom. If I don’t use a broker, I can go up to 1800$/month. If I do, max would be about 1500$. I plan on looking at Williamsburg, Greenpoint, Park Slope, Windsor Terrace, Kensington, Boerum Hill, Cobble Hill, and Carroll Gardens. I would have to make a commute to Manhattan almost daily, but commute time is not so important as most of my classes are not early morning.
Above all, I am asking for any and all advice anyone can offer. But also: WHEN should I start looking, and when should the new lease ideally begin? I need to move in before school starts. A little overlap is OK, I think.