They are very popular here in Australia and have a reputation as being calm, easy going horses good for beginners. I dont necessarily agree with the last bit.
Certainly they are generally easy to handle on the ground, if they raced they have been exposed to many things, different locations, crowds, dogs, beach, on trucks, on floats. Many are ridden as well as worked in harness throughout their racing career at all three paces which can be lovely when introducing him to his new life as a ridden pleasure horse. Others have only ever worked in harness and always been discouraged to canter but these generally take to saddle training fairly happily.
Most people retrain them not to pace, preferring to work on establishing three solid gaits at walk, trot and canter. They are very capable of doing so. The only advantage i could see in training to maintain the fourth gait of pace would be endurance riding. Some people enjoy riding the pace, most dont. Also bear in mind there are two types of standardbred, trotters and pacers. Often pacers are easier to teach to canter whereas trotters default 'go faster' is just a super-trot.
They tend to be unbalanced and very stiff, have no concept of bending and flexing. They need lots and lots of work before they become balanced in themselves and balanced with a rider and of course this needs to be established slowly at all gaits. Often a pacing bred stb will revert to a pace when unbalanced or confused. It is for this reason that i dontfeel they are good forbeginners, despite beimg generally good natured, a beginner shouldnt be learning on an unbalanced horse.
As riding horses they are most capable as a low level all rounder, quite suitable for hacking, or a pony club type home having a go at everything. At higher levels of any specific discipline they arent as competitive with the exceptionperhaps of endurance.
They can be a bit of a 'dope on a rope' and they are very heavy in the hand, both in groundwork and ridden. For that reason i tend not to get along with them so well, i am more accustomed to arabs and tb who are very light and responsive on the end of a rope. Having said that they are all individuals and i did ride one towards the end of last year that i really liked, very unbalanced and green but very light and honest. Most are - my boy Billy was probably the exception being heavy but also arrogant and knew how to throw his weight around. From the others I've met, most arent like that.