I've never owned one but have worked with some. The ones that had never been thru a race barn and were not excessively pacey to ride made wonderful recreational horses, especially for trail but I know people who do Training-level dressage and low jumping with them with gratifying success. Some are really awkwardly pacey to ride but I suppose that is also partly a matter of personal taste.
Some ex-racers make wonderful recreational horses too, but IME the average off-the-track Standardbred is significantly more chronically-lame and hurtin' than the average off-the-track Thoroughbred, except that since it tends to be in different body parts than with Thoroughbreds it is quite often overlooked even by some vets, sometimes to the detriment of the rider and very often to the detriment of the horse. Just because there is no obvious limp on one leg does not make a horse sound for continued work
SO many off-the-track STBs have serious issues with feet, stifles and hind suspensories. By no means all, but a whole lot, especially the older ones (because of the relatively lower-impact way they race and train, and because of their generally very stoic hardworking honest dispositions, STBs can be kept racing in poorer physical shape than most TBs can)
The ones I've worked with have had STELLAR minds and temperaments (making allowances for sometimes you have to invest some time teaching them to be a recreational private horse as opposed to a racehorse).
JMHO, good luck, have fun,
Pat