If it's 10 miles one way, that is a reasonably long commute, likely to take an hour each way, including loading/unloading, locking/unlocking etc. The most appropriate bikes would be a road bike variant like a cyclocross or tour bike, or a rigid (no suspension) mountain bike with street tires, or a bike specifically designed to be a commuter. You should avoid comfort bikes, beach cruisers, bikes with suspension, and fat knobby tires, as they will slow you down. If an otherwise suitable bike has fat or knobby tires it should be possible to replace them with thinner or slicker ones. The bike should have eyelets to mount fenders and a rear rack. You can commute with a back pack but it makes your back sweaty, and putting your stuff in a pannier or otherwise attached to the rear rack is preferrable.

See if you can find something suitable used at a bike store. You should be able to get a good starter bike for $200-$300 and then you can upgrade in a year with all the money you saved.