Conservatory blinds come in all shapes and sizes and the challenge is deciding what is best for you and who should create and install them for you. Unless you are a professional installer yourself, you will not want to try this on your own.
Create a diagram of your conservatory and measure as best as you can for the areas you can get to. If you have the building plans, you can transfer measurements to your diagram. Your next step is to visit a home improvement decor centre and look through all the books they have for different types of blinds you can get for your conservatory.
This is really more a research project at this point and if you have your measurements with you, ask to get some basic pricing on what it would take to order and install. Your home improvement consultant can, at the least, provide by-the-window pricing and estimate any odd shaped windows you have, based on a vendor you've chosen.
Base your choice on how a product looks in the vendors' picture books and also the longevity of the product, any warranties provided, and your potential usage of opening and shutting the blinds over a period of time. Consider remote control aspects as well for areas not easy to reach.
If you are looking for a colour scheme to go in your conservatory, look at cellular blinds; preferably double-cell with solar backing that is lightweight but one that will still protect your furniture and rugs from sun glare. You can choose from many different colours in this style as well as many options, such as pull up/vertical blinds which will allow you to customise the value of your lighting.
Look at woven and bamboo styles for a less formal look. Check if there are any new man-made materials on the market, made especially to handle sun wear.
A side note, the Conservatory got its start in the "...16th century when wealthy landowners sought to cultivate citrus fruits such as lemons and oranges that began to appear on their dinner tables brought by traders from warmer regions of the Mediterranean." From Conservatory came the development of green houses. In America, our conservatories tend to be called sun rooms. My father has a sun room off the living room in his Irvington home.
"The widespread construction of UK conservatories came to a halt with the onset of World War II. While the advent of insulated glass in the 1950s and 1960s saw the development of simple sunroom structures, it was not until the 1970s that creative architects and builders began to recreate the Victorian styling of 19th century English conservatories in smaller domestic versions using insulated glass."