Your linen looks better than the stuff I used for my first robe - broadcloth! I know that they are technically supposed to be wool, but I've also seen some nice ones made of cotton twill.
I don't think stitches showing is that big of a deal, as long as the hem isn't too wide. It helps if you match your thread really well to the fabric. Another option I wanted to recommend is to leave the edges of the hood, sleeves and hem unfinished. I was watching ANH the other day and noticed that Obi Wan's look like they are unhemmed. I would assume that's either from wear and tear, or after all those years living in the desert, he just stopped caring and made his own that way.