It is difficult to make a recommendation about any behaviour issues unless one has seen them oneself. That being said, I've ridden an ex-race horse for years - and she is far calmer and steadier mount than most others I've been on. I'd be more concerned about someone getting hurt on the pony we have now due to his nature than I ever would have riding her. So I wouldn't use her previous track history to gauge her steadiness as a mount.
Personally, I would have a trainer come out and ride her - work with her for a little bit - and then have them give you a recommendation on if she will be the horse for you. Hopefully you have a trainer that knows your style, preferences, and ability, and can give you a well-grounded recommendation. I would also ask for the medical information/vet contact for when she was injured. What was the injury, it's extent, severity, etc. It doesn't take much for a horse to be retired from racing, and often an injury that would get her retired would never affect her being ridden as a pleasure horse.