Get insurance quotes for the cars because especially for a teenager the cost may vary a lot more than you might expect.

Corollas are great but it cost over half of what a new Corolla would cost and even if that is what they are selling for I would a hard time bringing myself to pay that much for an 8 year old car with basically 100k miles.

I did a quick google and the 2013 Impreza was one of the cars which Subaru had with a oil consumption problem so I would want to research that a lot more before buying it. At the very least if you get the imprezza the oil level needs to be checked every time you get gas.

I had an Honda Fit which was a few years older than the 2013 which you are looking at. It had the worst headlights of any car I have owned. Make sure that the headlights are not fogged and consider putting brighter bulbs into the Fit even though they will not last as long.