I think a lot of places you take lessons use the nylon skirts. It makes sense for people that have never had a wet exit before and it makes sense to have kids use them for a while, but once you're really going through rapids and big wave trains it makes a lot more sense to have a neoprene skirt. Go for a bungee, they're easier to put on (I made the semi-mistake of buying a super rugged rubber randed [say that ten times fast] skirt, and though I love it now and it stays incredibly dry, I realistically could have gotten away with a bungee rand pretty happily.
When you flip, and you miss your roll, natural instinct takes over and you pull the cord and swim out, because, naturally, you don't want to be in that boat anymore. If it really freaks you out, put the skirt on and practice pulling the cord when you're out of the water. Then practice a wet exit a couple times with your skirt on. It's really not a big deal.
If you have a minute and you feel up to it, check out this rant on women's specific spray skirts: