Well, I think the variety of responses you've gotten just reflects the variety of people's comfort level on steep terrain. You've gotten good advice, though - as much as possible, try to be upright, with your weight over your feet. For the most part, your grip will come from friction rather than footholds, so having your weight directly over your feet maximizes that. You can reach your arms out to balance and grab the occasional hand hold, but the more you lean into the rock, the more your feet will tend to slip.
As for rock shoes, it's kind of a zen question. If you have 'em, odds are you won't need them, only because you've probably climbed a bit, have good technique, and could go up it in sneakers. (Actually, that's not as crazy as it sounds. Since most of your grip comes from friction, a softer shoe that contacts the rock as completely as possible is preferrable.)
If you don't have them, then you probably haven't climbed much or at all, and the sticky soles would be nice. But, rock shoes are notoriously uncomfortable for long walks, which is basically what this is, so myself, I prefer my old five-tennies for slides.
Anyway, it's not like you're goint to "fall off" it. But, there are certainly some places where I wouldn't want to fall because you might roll a while before you came to a stop! But people climb it all the time in various degrees of preparedness, and accidents on it are pretty rare, so that should tell you something. Enjoy it - it's spectacular!