Jan, what side is the proper side to stand when showing showmanship at the starting cone?Well, this is a really good question because there is no written rule directly governing the answer. The only thing you must remember is not to impede the judges' view as you have pointed out and know where the judge is at all times. If you use the quarter method correctly, you will not go wrong on either counts. Note, although it is not required to use the quarter method, it is really the only way to ensure a correct showmanship presentation
Such as if the Judge is on the off side (right) of the horse, is the left side proper, as to not impede the judges view? If the judge is on the nearside at the start of the pattern, is the off-side the proper side?
What if the pattern is a straight pattern, such as all of the cones are in a row, so the judge is standing in line with the horse at the starting cone, what is the proper side to stand on?
NOTE FOR 4H - It is included in 4-H rules that the handler not obstruct the view of the horses hooves from the judge or ring steward. I do not know the origins of that rule but I would not think much of it. If you are aware of the judge and you are using the quarter method, at no time would you obstruct the view of your horses' hooves. This is a 4-H ONLY rule and I just wanted to make a note of it although it is fairly irrelevant.
So when setting up at the first cone, you are correct. If the judge is on the off side (right) it is proper to be on the left side. If the judge is on the near side, standing to the right side would be correct. When setting up for a pattern that will be performed in a straight line, and the judge is standing facing you maybe at the end of the line perhaps, then stand on the near side. This will make the lead off into the pattern more smooth since you will not have to cross back in front of the horse once you are approved to start your pattern. The least amount of movement is best since it will reduce your chances of faults. It is not incorrect, in this situation with the judge facing you to set up and then wait for the nod from the off side but that is an extra move and you could make a mistake when you cross over. Extra moves do not mean extra credit.
One thing I'd like to say here is that as long as a pattern does not call for a horse to stop and back up very near to the first cone, it is proper and very advantageous to move to the first cone, set up and be ready as soon as the exhibitor on pattern moves off the starting marker. This would be an advantage for you to take that extra second to set your horse up while the judge is observing the horse on pattern and not you. It's also nice to score a horse that has moved to the line up and then look up to see your next exhibitor ready, not setting up their horse.