I either purchased the Industrial Super Permanent markers at WalMart or Office Depot. Since they are truly fine-point, you don't have to worry about the breath of the writing either. I have never used them on mini-blinds, but I would think they would last as long on this surface as any other. I do have some mini-blinds (put up in the attic, thinking they might be good for something one day), so I will see what this looks like.
For my tropical plants, I do my own custom laminated labels, but I know that no one will go to the trouble and expense to do what I do. I use the Sharpie markers for my vegetables and non-tropical plants.