I was wondering if I examine the do I get to pick whether it becomes the or the ? Then I wonder if I do examine/transform it can I transform it back to the original picture or not? Can I transform it amongst the 3 indefinitely or am I stuck with whatever I examine/transform it to the first time?
I tried looking it up on Subetalodge and reading older threads, but nothing was clear for me.

for other things with a transform option, you can transform them indefinitely. I'd assume it was the same way but I'm not completely sure
Yes it is the same way. You can transform as much as you want to the picture in any of the three options proposed.
EDIT : That's why if you were to buy it from the SS (I assume you have it as you saw the Examine option), it would be better for you to buy the Picturesque Beachside Photo at 6m than the Ocean Wave at 15m. Same for most transformable items. Just check on Subetalodge all the "transformations" and buy the cheapest one.
That's why I was asking, I wanted to know before I tried examining it.
Thank you so much! That's what I thought, but I wanted to make sure since it said examine instead of transform.

No problem. I know it can be confusing. I wanted the Ocean Wave so badly when I was a kind of newbie and I was like "hot darn that's expensive !" and I figured out it was a transformable item. It felt great :P Have fun with your background and have a nice day. (: