I have ringlets I wear straight (glossy straight, glossy wavy, glossy big curls)... all need to be achieved with a straight iron. I swear by mine, I'm that unwilling to lose it. LOVE IT.
What kind do I use?
ANY straight iron that is 1 inch or less in diameter and goes up to a minimum of 430 degrees and has beveled edges. The small diameter allows you to go into the roots, and allows you to use it as a curling iron as well. I've used dozens of straight irons. If they have the heat potential (430+), they work. If they're beveled they keep your hair from bending/breaking. Biggest trick: set high and swipe ONCE rather than lower and keep making pass after pass.
Now... I also have super curly hair, so it may not be applicable, but I ALSO use Paul Mitchell Super Skinny Serum as a heat protectant / humidity protector. INVALUABLE.