Sounds like a great idea . Have also built a small games room recently (only fit in 2 arcades and 3 pins) and insulated the crap out of it to keep the room cool. It works pretty well most of the time.
Have got an split system air con in the house and you are right in regards to the install, as I was going to do it myself. Then a friend of mine who is a sparky offered to do it instead when he heard of my grand plans (also my complete ignorance). Just as well as once we started I realised I had bit off more than I could handle.
He had done many split systems and even then it did take most of the day with plumbing etc. I think you would be looking around the $400-500 mark for the install. Also need a registered sparky to do it for the warranty, as they ask for the installers electrical licence number.
So the box type may be more affordable and could do it yourself. Would need to match the output in relation to the area to cool. The systems normally advise as to the cubic area they are effective up to. Good luck with whatever you choose.
