Can you add in floor heating? If so it would open your options. If not and you live in a cooler state the carpet for sure. I'd go wall to wall.
I had a company carpet my concrete lower level and they did not use glue. I'm not sure if this is standard but it looks good even after 7 years.
The main thing is to be sure the carpet is secure somehow at every door way so it don't kick up.

Hi! Not all floors have to be glued down. A few options are carpet, hardwood (installed the floating method), and even luxury vinyl plank. Luxury vinyl plank is a great alternative to hardwood if you are on a budget. They have some great wood and stone looks, and a lot of them can be floated right over the concrete. For some inspiration, take a look at these vinyl planks... http://www.ivcfloors.com/Flooring%20Inspiration.aspx

One of your criteria for flooring will be the heat range this floor will be subject to. How cold/hot is your climate? Indoor flooring products have limitations...and most of them have to do with temperature range.

If you go onto any "installation instructions" sheet for any floor product, you will find the "indoor living temperatures/humidity" must be followed to maintain warranty. These numbers are normally found to be between 59 - 82 degrees F (15 - 28 Celsius) with a relative humidity between 45% - 65%.

How close this space stays to the indoor "ideal" is what will help determine the right solution. In cold winter climates, laminates and many vinyls are not an option because the adhesives used to produce the floor can not withstand temperatures below freezing. The opposite extreme is also true. Hot climates have problems with flooring reaching temps above 82 F. The adhesive holding the product together begings to reliquify around 84 F...which means the floors warp, bubble or even delaminate in extreme heat.

A tacked down carpet is one way around adhesives if you live in a cold climate. If you are in a hot climate than you can look to most forms of mortar-in-place flooring.

You could stain & polish the concrete.

Is this flooring fade resistant? We live in Ohio and have a 3 season room that is not heated or air conditioned. The original flooring is decking and there is carpet on top of the deck which I hate so we are looking at other options. We considered Karndean luxury vinyl and some of the other brands but they would not sustain the fluxuation of extreme temperature changes. We are thinking of ceramic tile but it is cold and hard on the feet. Thank you for your help!

Based on this discussion I purchased Mannington Adura Rigid. They claim to be able to handle extremes of temperature. What they don't tell you is that unless you install over a concrete floor, it warps. Company refused to honor their warranty because of that.

@egoldstein160 - thanks for your post. May I ask - what is your subfloor? and where are you located? have you found a better flooring solution?

I am in the same predicament - looking for vinyl flooring for a 3 season room.

I heard TARKETT has a product made for 3 season rooms.

Subfloor is Trex as it is on the 2nd floor. Finally decided to go with outdoor porcelain tile, as I read it is perfect for extremes of temperature. Flooring installer put a subfloor on top of Trex. It looks great. I am in mid Atlantic region so we have hot summers and some cold days in winter. No manufactured vinyl product will work in this scenario.

Outdoor porcelain tile was the right solution. it has weathered all seasons without any problem and looks great.