I am a "bit" of a bit connoisseur. My husband has finally relented about my bit collection!
We get the majority of our bits from Iowa Valley Carriage. One item that I totally recommend is the Bit Fit. It is a wonderful tool to measure horses' mouths, including their cheeks.
Recently (in the last 7 yrs. or so), I have found out more about the conformation of a horse's mouth. Horses' mouths come in as many different configurations as their legs or backs. Depending on how a mouth is formed will somewhat dictate what style bit they prefer, which is why there are so many bits and why no bit is the "magic" bit.
I have a mini gelding with a fleshy, thick tongue and lips (that sticks out between his teeth), and a very low palate (I can't get a finger in between his bit and the roof of his mouth. Consequently, he CAN'T STAND a jointed mouthpiece, as they pinch his fat lips against his teeth, bump the roof of his mouth, and squeeze his big fat tongue. I have tried a single jointed, big french link, little french link, Myler knockoff, etc. He is quieter and peaceful in a solid, leverage bit on a mild curb setting. Out of desperation, I used my big horse's 5" low port Kimberwicke, and my fussy horse totally calmed down and quit chomping. So then I used a 4" mullen Liverpool (figuring that I couldn't logically show in a 5" bit), and he was better, then I tried a 4" low port Liverpool and he was better yet, but not great. This year, a friend gave me a 4 1/2" Arch Butterfly and he found his happy bit! He was light, responsive, calm, didn't argue for bridling, etc.! This all happened over the course of two years. One thing that I learned over the experience is don't discount the width of the face when measuring, which is why the bit fit works so great. I know that Alax doesn't like snaffle bits, but he also appreciates the wider bits. I did have a judge comment on the width of the Butterfly, but then said (before I could say anything) that he seemed to be going along fine in it. We won all three of our Turnout classes this year, so if you find the "right" bit, a good judge should recognize this. It's just too bad that AMHR doesn't recognize these issues and allow leverage bits. We just show ADS shows and CDEs right now, so it isn't a big deal for us. (I should try a snaffle again, now that his mouth and training are further along to see if he will still be fussy.)
Our other minis go well on just a plain mullen snaffle. We have one gelding that is a little stronger, especially in cones, and therefore he goes well in a jointed snaffle.
I highly recommend putting the bit in your horse's mouth, getting down on your knees and looking and feeling how the bit operates in your horse's mouth. I learned a lot from that experience, just watch out for the teeth!