All my guys tend to be OTTBs. I generally start with a Myler mullen mouth with a curved mouthpiece. It is a different enough mouthpiece from what most racehorses go in that I find they don't dig into the bit as much as with a jointed snaffle.
I work from there: my current OTTB did not particularly like the mullen, and he needed steering, so I switched him to a copper mouth single joint full cheek, which he really likes.
Another loved to lean on everything, so we moved from the mullen to a regular jointed snaffle (disastrous) to a lozenge (good for a while) to alternating between a Dr Bristol and a Waterford.
My late Rudy did the mullen for a while, but didn't really settle in it. Moved to a jointed Happy Mouth D and he loved that. He did not like a narrow bit--he wanted something he could really wrap his mouth around and hold-not lean, but hold, like a dog with a done.
The horse I leased this summer loved the Mullen and it was his go-to bit, even cross-country.
I consider the Mullen to be pretty much the mildest possible bit, so I start there and move on as necessary.