First I have to say I am bias because I love standardbreds! I have grown up in a family that breeds and then tries to repurpose them for riding. That said it depends on the kind of work the horse has had. I know a number of standardbred's competed at the World Equestrian Games in events like dressage and jumping. They are very versatile horses. They are going to be different from a OTTB in that the majority of standies are going to be a little calmer. They are use to being harnessed, worked, standing in harness and then warmed up and raced. The issue seems to be not in putting the saddle on them or the equipment. Most of your re-working is going to be done under-saddle. They tend to a standardbred spook which is that they don't really move their feet. Again, these are generalizations. There is a reason that they are used as Amish buggy horses its because the Amish don't really want a crazy horse to take them to church and back. You also look at where the driver sits on a driving back and its pretty close to the horses feet. You don't want to hitch a cart/wagon or buggy to a wild card.
You would have to work on things like turning and bending. They are use to making turns with a harness and cart so they are don't use their hind end as much to turn. There is lots of debate on how to train a standardbred to canter. Its more like telling them that a canter is okay. The best way is to get them out on a trail or long straight away and ask for the canter and don't punished when its offered. Most are driven in a snaffle. I would also ask why the horse is no longer at the track. I have a few horses that retired at age 3 because they did not want to be race horses. They legally have to retire a horse in America at age 14. Taking a standardbred that has been raced for 14 years and training him to canter can blow his mind. Which makes sense if you are told and punished for 14 year of your life for doing one thing and then someone comes along and asks you to do that thing its going to freak you out a bit. If you can, talk to the trainer/driver or groom (often the same person). They are going to have an idea on who the horse is and what habits it has.
The other notable thing is that they LOVE people. I took three of my horses to a four day equine event where hundreds of people walked past the stall. The horse that did double duty for two days in the stall was the same on day one as he was on day two. He was worried the first morning, then calmed right down when people started to stop and say hi to him. The horses I ride all come when called. I have a great trail horse mare that likes to get "face hugs". She puts her head on my chest and stomach and lets me wrap my arms around her head. She gives this sigh like "all is good". This is in part because they are use to be touched all over and they are sort of in your pocket. If you have more specific questions there are a number of books I could recommend.