I find wooden blinds are a popular style for sun rooms. You can tilt the slats and control the light that comes into the room, or close them shut and block out the harsh glare. Often I find the choice comes down to what the difference is between real wood and faux wood, or why you might choose one over the other.
For rooms that tend to get more light, like sun rooms, faux wood is a better option as the colors are going to stand up better to harsher conditions. Most faux woods are made of a thick PVC or polystyrene material which makes them easier to clean. You can just wipe them down with some soap and water! They come in all colors and even grains so you can get a style that looks like real wood but will stand up to the test of time. The only downside to faux wood is it can get very heavy at larger sizes; so for bigger windows real wood may be the choice for you.
For larger windows, real wood may then be a better option as at larger spans they can be easier to operate. Another reason why real wood is popular is the warm look it brings into the space. It comes in many different stains, as well as painted colors, so you have options for what will suit the room best. You can find colors to match the walls, trim, or even the floors and furniture!