Welcome to AH!

Don't worry if your question seems very basic- you picked the correct place to ask it! I'm not that familiar with those Mirages, but I don't think there's any reason they'd present any special problems to sub integration. Certainly the Hsu subs you mention are superb subs. Don't worry too much about auditioning them in a store- your home is really the only environment that's relevant, and you just can't tell how it will sound in the store.
A few internet companies come to mind: Hsu Research, Adire Audio (their 'Rava' sub would probably fit the bill very well), Outlaw Audio, Axiom & SVS. All these companies make very good subs, plus all offer excellent customer service. The best part is that they all have very good return policies. So if the sub doesn't perform well in your home, they'll let you return 'em with no hassle. Some will even refund shipping. If you go that route, they can easily give you exact dimensions to be sure it'll fit (although that shouldn't be a problem- 27" is pretty large).
Adire Audio is very big with DIY'ers, and their 12" Shiva sub driver is
legendary. They sell kits for DIY and have a forum dedicated to making your own. Dan is a really good guy and will help you out if you go that route. Honestly, though, there are such good subs you can buy in the same range that it almost doesn't pay to build one, except just for the satisfaction of rolling your own.
As far as placement goes, if you post a diagram we'd be happy to chime in with suggestions. Those ceilings are pretty high, which can be a good thing, but it will increase the room volume, requiring more power to pressurize. It'll also move the room modes around a bit vs a more standard 8' ceiling. Your room is close to square, which means some bass traps might be a good idea.
A sub will really make your home theater come alive, and it'll REALLY supercharge your Xbox gaming! There's nothing like cranking up some MechAssault or HALO with a good sub to rearrange the furniture.
Let us know if we can help you out any further.