Is there a trainer close by that you could take a couple lessons from to help you start out and continue with occasionally through the process? If not, there's lots of good videos on YouTube you can check out, both on teaching and watching others patterns.
Look up at where you're going. Don't do the waddle run. Hands closed/thumbs up on the lead. Make sure your hair is in a neat bun. You don't need a 2k jacket but you do need to wear something well tailored and clean. Also there's a few different ways to cross over for your quarters, find the one that's most graceful for you personally.
You want the horse to work off your body, not the chain. But the horse also needs to respect and give to the pressure. If horse doesn't already, spend some time just working with give to the chain. Of course working off your body isn't 100% possible at first as they learn but remember that as you're fine tuning. Especially when stopping, this will cause the horse to throw its hip out and your straight line is toast.
If you're trying to do anything straight it can help to pick a point on the wall/fence/etc to focus on going straight towards.
The pivot is a FORWARD motion. To get plant on the correct (r hind) you need to be forward. Start slow. Reward the horse crossing over in the front. Then reward a couple steps etc etc. Your setup should also be a forward motion if you need to adjust.
Backing is important too. If you can back your horse through maneuvers, you can back straight. As with other maneuvers, start with a step or two and reward the give/correct motion. Also don't stand in front of your horse when you back. It's occasionally done across all levels but that doesnt make it correct. It looks bad, and is very dangerous.
Grooming/turnout is important too. I don't recommend hoof black unless at a very large show as it dries the hooves out pretty bad. A bit of baby oil as face highlighter, corn starch on white legs. Well clipped, no stains. Make sure the halter is well fitted and correctly placed, not loose and hanging off the nose.