P.S. I would have to chime in with what other people have been saying - if you put decent slick tires on your mountain bike and either lock out the front shock or set it to it's least-bouncy setting, it's unlikely the new bike you linked to would be much of an improvement over what you already have.

I think you would need to go to a road bike to get something substantially faster, and if there isn't anything on craigslist, entry level road bikes from a shop are more like $700-$900 for the bike. If you find an older model you might be able to bring that down a little, but it sounds way out of your price range.

If you're looking for a specific tire recommendation, from reputation the cheapest-but-reliable-and-puncture-resistant tire I know of is the Panaracer Pasela TG:
http://www.rei.com/product/764318

(If you buy a Pasela, be sure it has Tourguard or TG in it's name or you'll get the non-flat-resistant one).