My search-fu is weak today.

What if only one gem is attached? (We'll say Soul Gem for this example).
Beginning of my turn, #1 is showing, I pick Soul Gem. Next turn, I can't pick Soul Gem again. So if you choose to stay on #1 with only one gem attached you can only use the gem's effects every other turn.

Is that correct?

That is correct, unless of course the gem is showing on the dial as well.

Right. You're choosing from what is available through being on the Gauntlet and not chosen last turn. So one gem will only allow a choice every other turn.

Actually those are both wrong (sorry) according to the latest players guide the correct wording on the power is: At the beginning of your turn choose a gem that you did not choose during your last turn. Character can use the effects of that gem as long as this power is showing. So the way it works is that if you only had the soul gem you could choose that gem on the first turn and as long as you are on that power you can use the soul gem. If you have more than one gem attached you can choose a different gem the next round and use BOTH of them and so on and so forth...you are literally powering up the gauntlet it's pretty boss.

That is not what the player's guide says. It says:

Beyond Mortal Limits: At the beginning of your turn, choose
an attached gem that you did not choose during your last turn.
Character can use the effects of that gem until the beginning of
your next turn as long as this power is showing.

You still only get the gem until the beginning of your next turn, but if that character acts (receiving an action token) and you roll for the gauntlet and end up clicking off of power 1 and onto power 2, you now no longer have access to the gem you chose.

but with special power #1 showing you dont have to do anything, option 3 allows you to stay on that click till you decide to roll or take a click of unavoidable damage. So in theory you could stay on that click of the gauntlet dial while picking and choosing the gems that might or might not be showing based on the click you are on and what gem(s) you have attached.

That's true, but remember the question relates to being on special power #1 and having only one gem attached. In that case SP1 will only allow you to choose that gem (he said Soul Gem, so we'll go with that), and only every other turn. If the Soul Gem is attached and showing on the dial you can use it from there every turn, but that' not the question.