You'll find many of us really aren't fans of tom thumbs, they confusing and pretty harsh actually. Wonder bits are okay but I don't really like them either, it's one of those things that is personal preference on them.
If you are just getting into it I would suggest shopping for a Jr. Cowhorse Bit myself, a bit choice I'm sure other posters will approve of :)
As for my horses, I primarily use a small set of bits. A smooth snaffle, a smooth draw gag, a Billy Allen shank, a loomis, most of the Jr cowhorses (Except the single joint twisted), Sweet Six (Iron wrapped lifesaver or smooth) and a ring combination bit.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.