It also depends on the length of the chain you're using. I string mine through the left loop, under, up through the right and clip to the top right one, as in the photos you provided, but if the chain is longer and it is leaving a long excess hanging that will end up giving you less control in the end, you can always string the clip through that top hole and back down to clip on to the lower right side hole (hope that makes sense)
I usually loop my excess and hold it in the middle, so it looks like an 8, but for local shows whatever you do- figure 8, loop(as long as it isn't big) basically make it look neat and not super floppy and you will be fine :) asking other people in your classes how they fold theirs works too.
Practice, practice, practice! also remember that the 4 quad rule always applies to you- even if the judge is at the other end of the arena with another horse, so you have to be alert. And always smile! Even if your horse is being silly and not doing the moves correctly, if you have a genuine smile and great posture, that is always a good mark in the judge's eyes :)
Details. When crossing in front of your horse as the judge does their inspection, try to keep it to 3 steps, don't look like you are running or shuffling your feet a bunch. The crisp quick transition just looks better. Practice practice.
And, of course, have fun. It's hard not to with a smile on :)