room style has lot to do with your choice I think because that is lot of wall space-- you have privacy beyond the sliders into the backyard--doesn't look like you have problem with neighbors overlooking your house too badly.. if you have a more contemporary/electic type of look in mind, consider using cable for one long curtain rod---and have sheers on rings--with lot of fullness-- you can add stops along the cable line so that sheers/panels can only go so far in either direction-- meaning they would stack where the wall separates the sliders when they are open doing that would make it easier to keep same amount of covering in each section cable can be in almost any metal finish to go with your hardware in the room--like door handles/cabinet knobs check out the website for Cote de Texas she has some good photos of similar window treatments

What are your needs for the WT? Looks, privacy, light filtering, block out? Since it's the dining room, a pic might help to visualize the space and your own style. I have 2 sliders backyard facing. The one in the kitchen/family has no treatment and I prefer it that way; in our master bedroom we did layered treatment with a double traverse rod with center opening pinch pleats on top and sheers below for light filtering/privacy--above that I plan to hang a valance when DH gets around to it. As I wanted the center opening, I took them about 15" beyond the door frame so when open they stack back behind the door. Before I had them all go to one side, but I like the symmetry of this arrangement better. If you do decide on a fabric treatment you can tie it in and dress up the wood blinds with a coordinating valance or roman shade. There are other options for vertical blinds (some with sheer material in between), bamboo, etc. Check out the JC Penny website for other options. Here is a link that might be useful: JC Penny draperies

For a transitional style room with sliding doors I'd do floor length curtain panels on each side, hung on a rod located half way between the door molding and the ceiling.

In our new house we used Hunter Douglas Duettes (wired & automated) with top-down/bottom-up for all the windows. On 3 of our sliders we use the Hunter Douglas Vertiglide shades, basically duettes that are vertical. Depending on the room, we used opaque or room darkening fabric. Very happy with all of them.