I have a 13 mile commute, and I'm looking to buy a new bike
Used. You can find some decent used bikes in that range.  A hybrid might be a good choice.  You find people that paid $800 - $900 for bike they never used and it will sell used as low as $300.  Be patient and low ball.  Learn how to inspect a bike.  If you are on a budget you need to learn how to maintain a bike.