Sorry for the confusion...

I was quoted $240 a month for full coverage. (They have a small discount if you pay 6 months at a time, but its like 20$)

The $350 a year is for liability only, does not cover your own vehicle.

Edit: If you take a loan out, you must carry full coverage. If you pay cash, or have the title in your name with a high rate loan, you carry whatever coverage you want. Liability only is the lowest coverage.