First I would encourage you to read the thread for beginners: Barrel Racing Exercises and Drills.
You can teach Dixie May some basics about barrels on hard clay, but if that's truly the only ground you have to practice on, I wouldn't go any faster than a trot. Barrel horses need to be able to dig in for footing around a barrel, and if you are practicing on a hard surface, that does not work well and puts their joints at greater risk for injury. Yes, it's true that some rodeos have trashy hard ground. But there is a big difference between running a trained, experienced horse on rodeo ground, than expecting a horse to learn barrels from scratch.
If you can get at least a couple lessons, here and there, from a professional barrel racing trainer, that will be of great help. Training horses is "hands on" and you'll get better insight from a human being in person, than over the internet.
Key thing with barrel training is to go SLOW. Yup. To train for a speed event, slow is key.
Also, make sure you can control every piece of your horse's body. Nose, neck, shoulders, ribcage, hindquarters. If you can have that precise of control at slower speeds on the pattern, you are going to need it when you are going Mach 90 at a barrel and realize you need to make a split-second adjustment.
Good luck and keep us posted.