Buying my first car in Rochester

I have gone through my whole first semester here without a car in Rochester and it is very restrictive. I wanna buy a car that gets the job done, doesn’t have too much maintenance cost and is good enough for Rochester winters and snow.

I wanna spend as little money on this because i wanna Uber/DoorDash to recoup the money I spend on this.

Where should i look? Is Craigslist and marketplace valid or should I look at proper dealerships. I’m not a car person and this is my first time, so what brands, makes and features should I make sure the car has? I think a 2k-3k budget makes sense.