This is probably one of the toughest questions to answer as a window covering dealer. Sliding doors are tricky to cover but there are plenty of options:
Vertical blinds; this is one of the least favorite options. When people think of vertical blinds they think of the old ones that use to break all the time. I always suggest for a softer more modern look FABRIC vertical blinds.
Vertical Honeycomb Shades; this is probably one of the most practical. You have no cords or chains to pull they are like regular honeycomb shades that slide from side to side. Easy to open and close.
Roller Shades; for a modern clean look this is a great option, specially motorized. Keep in mind you have to wait until the shades rolls all the way before using the sliding door.
Shutters; this is another great option you can have them slide or bifold to uncover the sliding door. Great option but it is bulky requires a 7-8 inch frame around the door to allow for louver clearance.
Panel tracks; like roller shades but instead of rolling up they are panels that slide from side to side. Downside is a panel might cover part of the sliding door all the time, unless you have enough wall space where the panels are sling to.
Keep in mind ease of use when deciding to cover your sliding door. Also pets, kids and privacy are important.
Hope this helps,
Oscar
Aztec Blinds and Shutters