Window treatments..help!

Without seeing the room it's hard to say.

Room darkening Roman shades are used a lot on the decor shows on HGTV.

Stay away from those blinds, they are too hard to maintain. There are much better blinds on the market try Blinds Melbourne for the full range or click Melbourne Blindsto get a quote from them directly. Its usually cheaper than doing it yourself and you get a 2 year warranty. worth a try

HI Slickracer

Cellular shades aren't any harder to clean than most other treatments. Regular dusting with a feather duster. You can also use the brush attachment of your vacuum or even blow off dust with a can of compressed air. If you need to deal with stains, blot with a damp sponge and a very mild soap.
I think they are a good choice for a sun room, and you will love the top down bottom up feature. I recommend cordless, easy to use but you won't have all those cords hanging all over (2 cords per blind.) Is the patio a slider or french ? If slider I would look into a same color vertical cellular. Have fun.