One of the great things about a bike like the Street Triple (and most UJM type bikes) is that they are very versatile and can be ridden however the rider decides, and that doesnt have to be just one way either.
I commute daily to work 130 miles and if I rode the bike like a SS, all hunched over and pretzeled, it'd be a pretty uncomfortable ride, so I sit back a bit more, use lazy handlebar steering and just enjoy life.
On the other hand, when I do hit the canyons or twisties, its a simple matter to shift the rear back, the body forward and really hit it hard in the turns. There does seem to be a handlebar right about where I'd like my head to be, but thats the nature of these universal bikes.
In terms of "riding style", as I mentioned, with a bike like this you can make your own. Be safe and enjoy the new purchase.