I just got back from New York! I did my fair share of braiding while in town thanks to a sweet write-up in NY Mag that called me "The Braid Whisperer". Thanks again NY Mag!
I found that my go-to products for braiding just about every hair type were Oribe's Sculpting Cream and a little bit of Rough Luxury Molding Wax.
Dirty hair is really great for braiding. What I usually do to make the braid last longer is start with clean hair and use products to give it the dirty texture. This way you get the roughness that dirty hair gives you without the oiliness. You can prep your hair by applying Sculpting Cream on towel-dried hair and blow-dry it into your hair with your hands. The Oribe product line is very concentrated so a little always goes a long way. Using a brush to blow out the baby hairs on your hairline is also a good trick to make sure the whole look is nice and clean before braiding. Messy braids are beautiful and romantic but they have to be the right kind of messy.
If you have a lot of layers, the Rough Luxury wax is a great way to blend them all together so your hair can braid more easily. I usually rub a little on my fingers as I'm braiding so it works itself into the ends as I go.