Where are you? Some countries have more "riding type" standardbreds than others. Here in Aus, we have a LOT of harness type standies and very few that are really good riding types - but a LOT of them can really jump! Depends on the level you want to do I guess, standies make GREAT lower level allrounders and with the right training can make really nice jumpers and eventers. You just want to make sure the dressage isn't getting too much for them because dressage is REALLY important now and a good dressage score is often the difference between first and outside of the placings! I find that VERY few standardbreds have a good enough canter to do really well in dressage but if you find one that does, and that isn't ridiculously long in the back (harness conformation, a long back is considered to be a good thing in a racing standy), I think you'll find you have a nice eventer.
A huge upside to the standardbred, at least in Australia, is that most of them have the most beautiful nature! My old horse was a standie and he put up with so much from me, you wouldn't believe. I'd have another one - for a pleasure horse or low-level allrounder/eventer - in a heartbeat.
Just don't jump before your horse is 4 at the very youngest and definitely no higher than 18 inches until it's 5. Jumping's really hard on growing bones and if you jump them real young their long-term soundness can be affected.