Trying to come up with idea for UI for sticker selection:
No luck.
I would suggest to approach this from a design standpoint that puts the visual aesthetic into consideration
at later stages after the core idea behind the layout is found effective.
For example, the image that fits best with the mechanic's purpose (assuming we are talking usability) is the
second one.
The entire purpose of this UI is to let the player pick the best "tool" to handle a certain puzzle or situation.
So in the second image you can clearly see the scene itself (one of the reason image 3 is not an option in my
honest opinion), you can clearly identify each individual sticker and you could work out in your head how to
put everything together and complete the task at hand.
Another thing that you should take into account is what are you planning ahead for the game, mainly if the sticker
concept is going to evolve in some way or stay the same while only the puzzles themselves are going to evolve.
Of course these two things relate to each other but the main idea can be put into an example like this:
Assuming that the stickers on image 1 and 2 are not placeholders, the first two stickers are the same thing with
black and white inverted. One thing you can do is have only one of the available, and later in the game introduce
a mechanic that allows you to invert the color of a sticker so that black become white and vice versa.
This is just an example but what I'm getting to is that if such thing is going to be implemented eventually, you
have to think about it when designing the UI so it won't seem out of place when it is added later.
After you have everything sort of planned out you would know how to not limit yourself with the design and it should
be easier to construct it with everything in mind. After that phase you can begin thinking about aesthetic changes
and adjustments that will not compromise the initial design.
Sorry about the wall of text and good luck