Don't practice the pattern too much - I think that's what gets barrel horses goofy about the pattern. Figure eights at the lope are a good exercise to do - hope you have a blast!
As long as you keep actual barrel practice to a minimum and when you do practice, do it at a walk, trot or slow lope only, you'll do fine. There's no need to practice at home at full speed. Remember to also keep your horses mind fresh by doing other things too. Trail riding is a great outlet for all horses. Even pushing some cows can be good for a barrel horses mind, just something that isn't the same thing all the time and you're horse won't get resentful and burned out!
Chasin' cans sure is fun, I can't wait until I've got another one ready to do so. Good luck!
What I do is I trot to the first barrel, then when I get a few feet away, I walk. This creates a "pocket". I do it with all three barrels. But when we're geting ready to go "home" I walk him. I don't think horses need practice running in a straight line. And when the horse do get the pattern, don't do it every day. The get too sour. Sour is when the refuse too do the pattern and if you go to a competition, the might refuse to go into the arena or they start rearing and bucking so they don't have to do the pattern
What I did was I would trot the pattern, but every time you go around the barrel take them down to a walk so they know to slow down around the barrel or else they run right past it. Then you lope the pattern and trot the barrel and so on and so forth so they know to gather themselves up at the barrel. Work on lead changes a ton and your whoa's.
Everyone here has such great suggestions. Mine is that try your hardest to keep your horse calm and quiet. Keep him in the softest bit possible. I use only a full cheek twisted wire snaffle on my mare. And sometime I add a running martingale. One thisng I hate seeing are good barrel horses gone bad because all the rider did was jerk on the horses mouth. If you teach your horse the pattern and make it nice and slow and enjoyable, you shouldnt need to put your horse in a harsh gag bit or anything like that. After every run, if possible, have your horse walk the course. This will teach him that its okay to go slow. I also take my mare out on a trail ride after ward. It slows her mind down and keeps her mind on something other then barrels (she raced in the PRCA as athree year old)