Dee ring snaffles and Full cheek snaffles are the most popular style of snaffle for hunters. They come in a wide range of mouthpiece styles, a lot of horses prefer a french link style mouthpiece.
I personally love the look of my full cheek, and it helps push Cowboy around them turns :p Loose ring snaffles are ugly, and slide through pony's mouth. I use a dee on Diamond (slow twist, for gentle hands!!!) And a full cheek on Cowboy (he's easy :p)
To start with go with what your horse goes in already, you can read the rule book for restrictions. But I've noticed that someone high levels (3ft +) Pelhams are the biggest fad. Shows how fany you are and how you can ride with 2 reins - could you tell the sarcasm? Don't do this unless you can actually ride with 2 reins