Some stb's can have difficulty learning to canter under saddle, a lot has to do with their muscle development and balance, and is simply a matter of building them up slowly. It is always wise to rule out pain issues and problems with saddle fit, as well as having some lessons with a good instructor who can point out and help correct any of your issues that are affecting or confusing the horse. Don't expect the horse to work well on small circles until it has developed the correct muscle and balance - trail rides are ideal for training standies in a natural non pressured environment, and many will break into a canter when going uphill as it is easier work:)
If you go the trainer route - make sure it is someone who has an understanding of the breed - or at least someone who appreciates them...run a mile from anyone who tells you that standies can't canter or make good riding horses as the vast majority of them can and do!
There are also some great dvd's at
www.horseproblems.com.au - one is re-training the standardbred, the other is track to dressage, the re-mouthing dvd and also training the leg yeild - all very helpful if you are doing the training yourself.
Good luck and please post some piccies of your new horse!
Michelle