Did this exact decision on our last place, and the slider was also on a dim side of the house so blocking light was never the issue. What I learned the hard way: skip vertical blinds entirely. The wands and carriers wear out, slats get bent when the dog or the kids brush past, and they rattle every time the door moves. Ours looked tired within a year and cleaning them meant wiping each slat individually. Cellular shades were the better call for us. They sit close to the frame, stack up tight so the view stays open, and dust mostly just sits on top of the cells where a vacuum brush handles it in a minute. On a north-facing door they also add a bit of insulation at the glass, wich helped with the cold draft we got in winter.
One thing I'd tell my past self: measure for an outside mount and check the handle depth before ordering. Our slider handle stuck out further than I expected and the first shade wouldn't clear it when raised. Also look for cordless or a top-down option if you want the light from the top half while keeping privacy low down, handy on a door that faces the neighbor's yard.