It's your first time with Bananas - eh?
:)

Bananas like most rhizome plants are survivors. But they do tend to shut down from what I hear and read, when the temps drop below 70F/21C. So if you are located in an area where temps are going to drop during the Winter, inviting your Bananas inside your Sun room would be good. Bananas are a tropical and don't respond to seasonality. They do however respond to temperature and sunshine. Keep those temps above 70F/21C and let get sunshine and they'll be happy. They'll tolerate direct sunshine, but for young plants, partial shade is a good idea.

You'll see examples in posts of this forum where folks insulate their outdoor Banana plants during the colder months. There seems to be some logic for that as most plants are constantly drawing up water from deep in the soil. This water will be warmer than surface temps and if they ( the plants ) are insulated, they apparently are better off with the insulation and will grow as hardy as on a warm day.

It's basically up to you.
If you're fairly houseplant literate, and your sunroom stays at a minimum of 50 degrees at night in the winter, you can overwinter fairly easily with most species of bananas. You will see a slow amount of growth which might be good for you anyway with the limited space to grow them in anyway. hibiscus and other tropicals will do fine in that environment, with the exception of diffenbachias, heliconias, and a few other tropicals which are more cold sensitive and can't go below 60 at night and should be in your living areas.
The only catch is that you'll have to take care of them all winter vs the fact that they will be higher priced in the spring. Good deals on plants this time of the year!
So now you can make a more informed decision.

I'd do both. Like Sandy said, bananas are on sale at the nurseries now. I saw a nice sized blood banana (4 foot) for $11. It would be over $25 in the Spring. You can buy up some now -- as many as you have room for. And then buy smaller Home Depot ones in the Spring. Soon your yard will look like this:

{{gwi:419126}}

thanks everyone! Thanks also bearstate for making me literally LOL :0)