Hi :)
I like the idea for your project, but quite frankly I find your price expectations to be unreasonable.
From what I understand your primary focus is to match the school/university (degree program or classes maybe) with the user's preferences, providing the latter with tailored results using various filters such as costs, location, aid package etc. Moreover your long term goal is to have mobile apps that would interact with the same database.
You need a database, a well-designed one too, a good ORM model for smooth interaction between DB and the backend engine - an MVC web-app with a RESTfull API that your mobile apps will use as well. Backend interface and functionality to add schools, programs, filters, maybe a user profile etc. The list goes on.
Why would you need Wordpress for something like that in the first place? That's shooting yourself in the foot :)
You need a web-app, coded in one of the mainstream MVC frameworks (Laravel, Yii, Zend).
I might be overthinking the whole endeavor and if all you want is a clean modern theme with a few basic filters parsing through your word document of universities, then I guess $300 is ok.
Feel free to contact