I start mine in a rope halter or side pull. From there I experiment. I don't have a go to bit as every horse is different.
My personal horse, Friska's first bit was a jr cowhorse with a chain mouthpiece. She would flip over backwards, rear and paw at the bridle to get it off, about rub her eye out on fences, itch herself with a back hoof etc with any other bit. She has the fattest tongue and lowest pallet of any horse i've known. There is barely any room for a bit.
However the first bit I try is a loose ring snaffle with a dogbone center, if that doesn't work i've got quite a few bits to sift through . Personally I am not a fan of full cheeks, if I want that effect i'll go with a baucher. Working for a trader I met one horse who killed himself while wearing a full cheek. The rider was just relaxing on him talking to another rider in the arena. The horse turned his head to bite a fly and then itched himself on the saddle. He got his bit hung up in the D ring panicked and flipped over backwards breaking his neck. The rider escaped with a couple breaks. I know it was a freak accident but i've also seen horses get hung up in full cheeks while tied around ( which is also something I won't do) so I am pretty leery of them now and always opt for something that isn't going to get hung up on something.