Where you sit/stand in relation to the barrels can make even wide turns look better. Normally their 2nd barrel is the best and it's often difficult to get a good photo when they turn the top barrel unless you're talking professional riders. Of course it all depends on the arena access you have and sometimes you have to try getting photos from the oddest positions. One thing I've discovered over the years, wherever you stand you're never in the right spot for something.
I've worked in some dark arenas, we don't use flashes unless they are set up above where the horses will see them. Shoot at f2.8, high ISO, and you can get as slow as 1/320th shutter speed. Outside is so much easier.