Welcome to the forum Nike! Threads like this generally make me cringe, because a lot of times it's brand new riders looking for cheap mounts, thinking they can train it just because they can stay on a horse- but you sound like to have quite a bit of good, solid experience, and the fact that you have a trainer is even better.
Having trained my very first OTTB this year, ( NOAH
) I will definitely tell you that they are very rewarding animals with a lot of heart. Our boy was already older when we got him, as he wasn't retired off of the track until his teens (for what reasons, I don't know. He wasn't exceptionally fast)- but he has made a VERY solid mount for us and has been recently introduced to our lesson horse team.
Advice that I can give you though is, most importantly- make sure that you train your OTTB as if he has never been touched. A lot of times, racehorses are pushed into racing far before they learn any of their ground manners, and they have many gaps in their training that can make them dangerous if you don't fill those in. Very rarely will you find an OTTB who knows what to do with leg aids, and even more rarely will you find one with effective brakes.
Besides that, look for a TB with strong, well sloped shoulders and good bone. Many OTTBs that I've seen lately are built for their aerodynamics, not their soundness- and so many of them have very thin hoof walls and require special shodding or just aren't sound whatsoever. Also look for one who seems interested in their surrounding but not frightened. I think it is very wise of you to want to purchase an OTTB from an organiziation like LOPE, because they generally give you the plain facts about the animal without sugar coating it, and if I remember right they do a basic soundness test as well, and cover basics under saddle. Just remember though, that in taking in an OTTB, even if they're sound during a PPE, that doesn't mean they won't have problems arise later on. Many of them have artheritis set in early, or have weak bone and muscle structure that just can't take hard work. For this reason, I would advise in looking for a 3 or 4 year old that was only raced a few times then sold because it had no interest in racing. Being able to ride the horse is a plus as well, and many organizations/trainers are willing to let you test the animal out.
Other than that, all I can say is GOOD LUCK, And post plenty of pictures one you get your new guy/girl!