13 feet from eyes to screen? Ya gotta go as big as you possibly can. A 95" diagonal screen would be the SMPTE recommended 30° viewing angle size.
Is your room totally light controlled, as in, you can make it totally pitch black whenever you're viewing? If so, a front projector would definitely be the best choice. If you don't have light control, though, then the biggest flat panel that you can afford is the way to go