Don't forget a screen for the projector. also a projector mount and the installation may be hard to grab all that stuff for under 1k. I agree with the Optoma recommendation for a projector.
I would go with the digital coaxial converter like this one from cables to go http://www.cablestogo.com/product.asp?cat_id=3103&sku=40019&relatedItem=true# this is a better option then the selector because you will have no remote control of the selector.