The snaffles I have are these, and this is what all the training is done in:
Myler Comfort Snaffles, in all the levels they come in. I have them in smooth, and then a Level 1 Twisted.
French Link - Mine is an AlBaCon I believe, loose ring, and then I have a no-brand eggbutt.
Twisted Dogbone - Loose ring, only one of these.
Single Jointed - I really like the ones with copper inlay . I mainly have loose rings, but also D rings and eggbutts. Have one of these twisted, but if I'm going to go twisted I will generally do the dogbone or the Myler first.
Lifesavers - Probably my favorite, also my favorite mouthpiece for my barrel horses once I move up into another bit to run. REALLY love the Sharon Camarillo bit in this variety: Reinsman Sharon Camarillo Lifesaver Snaffle Bit - Horse.com
Edit: Totally forgot one, I also have a snaffle with copper rollers but I don't use that one as much because the majority of my horses tend to get more distracted by the rollers and go ADHD on me.