I think that leather bits are more of a fad than anything. Yes, some horses might like them, but they aren't any different, mechanically, from a chain snaffle. When you apply pressure, they wrap around the horse's entire lower jaw putting pressure on everything and because they are so flexible, they don't allow the horse to pick the bit up and carry it instead of just packing it around. Maybe not everyone agrees with me, but I prefer my horses to carry the bits themselves instead of depending on the bridle to keep it in their mouth. When they are carrying the bit, they can feel more of the cues that I send them. Leather bits aren't so different than those old war bridles that the Native Americans used to use, where they just tied a length of sinew or leather around the lower jaw and tied reins to it. It's not nearly as mild as most people would like to believe.
Anyway, for initial training, and even re-training, I prefer to stick with a simple snaffle of some sort, whether it's single jointed, French link, mullen, or even Myler/Billy Allen styles. I try to stay away from shanks of any sort because they just add more working parts and pressure points and increase the probability of confusion/frustration on the horse's part.
As for the Tom Thumb bit that you posted, that is quite probably the worst possible bit, especially if the horse you are using it on is having issues with rearing. The Dutch gag isn't much better because in addition to all the issues that the TT causes, then you add in a gag action. That bit has no place on a young horse just getting used to being ridden.
I would go with the French link full cheek that the one person suggested and use it on both of them until they are trained enough to be ready for something more advanced.
Then, when (and IF) they are ready for something more advanced, like some sort of curb bit, then I would suggest something like this. It has very short shanks, so it's very mild, and the myler type mouth give you more feel without being harsh.