I would stay away from the ductless or the mini-split system. We have those on a couple of buildings where I work to cool the telecom rooms. They are loud and the evaporator unit that is mounted inside the room leaks condensate every so often. The condensate reservoir is very small and if there is a lot of heat in that room, the reservoir will fill up and leak. Since you live in Georgia, I would suspect that it gets very humid in that part of the country. If the area you live in has high humidity, you are going to need a system that will easily cool the space while you and your family are enjoying a movie. Remember, the human body produces a lot of BTU’s of heat. There are HVAC systems called self contained or package air conditioners. These are a self contained AC or heat pump system with connections for supply and return duct work. The unit is mounted outside and the duct work is run outside to the conditioned space. So, all you see inside is the supply and return registers. There is no sound, no leaks, and is easy to work on. There is no fan, no evaporator coil inside the space. Trane, Goodman, Lennox, and York all make package system. I would check into this kind of system. They are the same price and the best part is, they come ready to run. They come with a full charge of R410a and easy to install.
Here is a link to Goodman to show you what I am talking about. Now, This may be waaaay to much cooling for what you want, but I am just trying to show you what I am talking about. I think they make smaller units, you will just have to ask around. I have seen many home owners have these installed. Down in Arizona and Nevada, these are mostly mounted on the roof of most residential homes because it gets so hot down there.