I'm in the process of retraining two OTTB mares and have re-trained a nice OTTB gelding, and I've used a variety of bits, depending on the specific animal's problem. I've found that full cheek snaffles tend to be the best though, because, as Rascalboy said- its nearly impossible to pull them through the horse's mouth, and they really help while teaching the horse to steer.
I'm using a full cheek french link snaffle ( this one
) on our extremely green mare who is at about the same level as your OTTB right now, and she seems to be doing really well in it. However, I don't use side reins whatsoever in any part of my retraining process, so I don't know how well it works with those.
I've also used a Happy Mouth Mullen D-Ring here
with our OTTB gelding, who had been on the track working as a pony horse for a year before we took him, and was already fairly good with mouth contact and turning. Both he and I liked it, though haven't tried it with any other horses so I can't say much else about it. Some horses like the solid feeling of the rubber though, so I'd recommend it if your OTTB doesn't like metal.