sure.. you should be able to buy an IO box that comes with a version of ProTools for that much..
I use cubase, but that's just what I with started many many years ago and I know it best.
For video \ film, if you have Creative Suite CC, don't ignore adobe audition it integrates very well with the other tools, has some very good out of the box noise reduction, multitrack etc.
I sugest you sign on with adobe production suite premium CC, its well within you budget (if you string out the payments for a year or two) plus you get a LOT OF THE BEST TOOLS for video. Adobe has great student pricing.. and very liberally with what is a "student"