Have you talked to your college tutors about what they might think?
Pro kit is pricey, and even mid-range dslr / csc camera systems for video are going to be way out of your indicated price range.
To learn video, though, incorporates learning storytelling (script) and editing as well as photography / motion photography, sound, and, arguably, graphics and effects. Your tutors may have a view as to where to direct any spare time, effort and money in advance of starting.
Maybe writing a few scripts (free with OpenOffice) would offer a different starting point.
Maybe even sketching out simple animatics with a drawing app or something like https://motionartist.smithmicro.com/tour.html#features if you have a drawing app. Even a demo of something like Anime Studio might tell you something worthwhile … https://anime.smithmicro.com/anime-pro.html
I’m guessing you must have studied on a film-related course already …?
If your focus is on photography / image production, the best kit you can afford (or can nearly afford, with help) could be your target. You’ll want decent movie quality, and as much control of the camera (manual control) as you can afford.
If your interest is in the storytelling and you are going to be working with a small group of contacts or friends to explore narrative or other film making approaches, then any decent cheap camcorder that will let you get motion pictures easily (pictures your computer can edit) might server you well enough. That way, you could make short, experimental films with the emphasis on story or style rather than tech quality, and could try out your ideas and learn a bit through doing, before you start your course, … and have a few shorts to show too.
At the extremely limited but possible end while likely to be still useful later, something like the GoPro Hero might bave an interest. No zoom though, very tricky sound … hmmm. https://www.jessops.com/online.store/products/89562/Show.html?utm_source=google&utm_medium=cpc&utm_campaign=PLA&utm_term=HERO3%20White%20Edition%20Action%20Camera&gclid=COjN2Of24bsCFRLMtAodVHkA9A