If you set the speed at 12 frames per second, you would only shoot one frame, then move the puppet. Then you put it in a video that plays back at 12 frames per second, and it plays at the speed you intended. If you want to upload to Youtube at 12 fps, just shoot ones, do the whole thing at 12 fps. The file size will be half as big because there are half as many frames as a film that plays at 24fps, and I'm pretty sure Youtube can do a 12 fps playback.
But if you were making a 24 fps film, and had the speed set at 24 fps, you would shoot 2 frames the same. Why shoot the extra frames, if each pair of them are the same? Well, it gives you the option of shooting on ones when the motion gets fast, then going back to twos, all in the same shot.
If it was in a film that was going to play at 24 frames per second, but you only shot 12 frames for each second, on ones, you could double the length to 200% of your animation in After Effects, so each of your frames would be repeated. Then it would look the same as if you had shot "on twos" for a speed of 24 fps. Shooting on twos is a term that dates from shooting film, where it would always be projected at 24 fps. If you wanted to only do 12 moves per second, you would shoot two frames.
Same with 12 1/2 fps and 25 fps. Broadcast video and DVDs always play at the same speed, 25 fps for PAL countries. If you were going to put it on a PAL dvd that plays at 25 fps, you would want 2 frames for each puppet move. So either you shoot each one twice (at 25 fps), or you set the speed to 12 1/2 fps and shoot only once, but then stretch out the duration of the shot to 200% in AE or your editing program so you get 2 of each frame.
Yes, shoot at 12 or 12 1/2 fps, on ones.
On second thought - you live in the USA, which doesn't use PAL video at 25 fps, so you don't need to use 12 1/2 which is half of that. Just stick to 12 fps, which is half of the film rate of 24 fps, because that is the same in every country.
So, shoot on ones, at 12 fps.