I recommend finding a good horse that already knows his job but can wait for you to learn with him and take you where you need to go. Start out with fun shows and work there. They are cheap. Eventually if you get really good, go to money shows!! I really like Charmayne James. I have her book and videos. If I were you, I would get them because they are amazingly helpful! Even for me and I have been showing a long long time!! If you have any questions, I would love to help! Just message me!
I would look for something finished, been there done that to ride. It you want to teach your horse, seek the help of a professional trainer with experience in this events. Gymkhana is a fantastic, low-key place to go play around in.
I had a friend who was into barrel racing and she taught me with her horse... I didnt know much and I trained my own horse... Its not hard if you want to learn with your horse (: Especially if your just wanting to do it for fun but Im sure eventually you'll really wanna go to a competition and in that case I think maybe you should just have someone who's done barrels before (not necessarily a trainer) to just come and help you. Hang out and have fun with you... Barrels is a lot of fun(: Go to a few rodeos and see how they do it that way you have an idea... or look up on youtube but don't watch the kids just doing a video of how they do it.. Look up the pros :)