I would recommend Dark Souls.
I played Dark Souls, followed by Demon's Souls and I think playing Demon's first would have soured my Dark Souls experience. Dark Souls felt absolutely groundbreaking, wholly unique, and incredibly refreshing. Had I played Demon's first, I would have already experience a lot of stuff in the first game that was done again, but better in the second.
Dark borrows a few great moments from Demon's but I think is more successful with it.
Basically, my view on it is if you want one, really impactful experience followed by two really great ones, play Dark Souls, Demon's Souls, then Dark Souls II.
If you're comfortable with dampening what is potentially a really revelatory game experience, then play in release order. Demon's, Dark, Dark II.
It is very true that whichever iteration you play first, and you are smitten with the souls format, you will likely figure that is the best. the Virgin expereience rules. I have even heard a few who played DS2 first say that it was the best of the series for them. Most seem to agree that its between DeS and Da1 for the more polished experience. THe open world in Dark with the collision map overlapping back on itself was genius, something that was an unexpected surprise, despite many DeS fans clamouring for an open world, no one expected THIS. Still the art direction and taughtness of Demons' is slightly better, despite other minor flaws that were corrected in Dark, while others were reverted to in DS2. Obviously many details are personal preference.
I guess another reason I liked the Demons' experience so much was the fact that no one had "done it" yet and the community was helping build the wikis etc. because each is game is so rich in tricks and traps and detail, I had the pleasure of uncovering a few things myslef and blowing minds of fellow gaffers....this was over the top fun as I love detective work, and figuring out lore etc was yet another nouveau thing for the community at Demons' launch. It would be very hard to re-create this, but perhaps there should be a thread started here for Demons' and/or Dark1 first timers who take and oath to media ban and see what they can figure out as a tight knit community. Select wisely my friends...dont allow poeple in who would cheat and spoil it by looking things up!
I agree with Alo81's appraisal as well though and you really cant go wrong with whatever you choose to do first.