Your choice of areas are great. As far as school areas, I would suggest, Old Bridge, Matawan, Sayreville and Aberdeen.
If you want to talk, give me a call. I can get some more information and hook you up with a mortgage professional if you need.
I will run a search and direct all my knowledge for you. Your price range is good, we can find many properties.
I work with Ellen Rosenbaum Real Estate.
My cell is 908 839 9634
And office 732 679 5661
I look forward to helping you out.