I would start off local, no reason to spend the extra time and money traveling so far, unless you have someone to coach you, I guess. That would be worth the travel, if you have a great learning opportunity.
As for your horse's trot, it might be helpful to think of the 3 'basic' types of trot you might be asked to demonstrate...the medium or working trot is what you enter the ring at, typically (sometimes the walk), and they might ask you to extend the trot, or collect the trot. So, you want to be able to show a difference between your regular, collected, and extended trot. If you are going too slow or fast to begin with, then it will be difficult to go slower, or faster (I say 'slower' or faster' but, really it is the collection or extension that should be demonstrated, but for ease of discussion, we'll say slow/fast
Also, funny that you have a red saddle pad, I mentioned that because I had a red saddle pad at my very first show! I had no idea what the norms were, so if people were staring, I thought it was because of my beautiful horse
It was the last show of the season, so the classes were small. I think there were 4 in each class, and I placed 4 out of 4. I was a little frustrated, because I didn't know why I didn't place better, but, it challenged me to find out, and therefore learn more, and become a better rider. I found a good instructor, and, although I could only afford 1 lesson every month or so, I worked hard, and was 'in the ribbons' at the end of the next year
What is funny, too, is that, a year before I started showing, all I wanted was a horse, and I didn't even dream of showing. But, one show was all it took for me to get hooked.