Why not a phone? Until late last year I did my channel entirely on the back of a Galaxy S6, editing and all. Took my channel to 2,500 subs, 125,000 views with a six year old phone. I assume you already have a phone but if not it may be worth considering to start out versus a camera.
I've sorta been looking for something like this too, but I am in high school not college. I have a camera, but I've had it since like 2013 (it was used by my sister too who did YouTube) so it's been passed around and used a lot. I do more of gaming style videos though, not vlogging so I probably need different equipment than you would. I do not have an external mic either, so I have to rely on either the microphone built into my phone or the one built into my computer. By the way, my phone is an iPhone X.