We have had vertical blinds for at least 15 years at least and would not consider horizontals as I have had to clean some in flats where they were fitted (son's digs, etc., some were wooden which admittedly somehow look better). You are correct, horizontals gather dust and, if present, also catch the tiniest droplets in the air (bathroom, kitchen, etc.) as they are pulled downward by gravity. Result: dust and even goo on the surfaces. We have never had to clean our verticals (much larger slats, no lines through them) except where something has been rubbed or splashed onto them.
In the end the choice is yours - have a look at places where they/each are/is fitted, then imagine them in your house. But on the cleaning issue puts verticals ahead on points.
Note to cloverjo: I am pretty sure you can buy the line and weights on eBay.