You will want to use Position keyframes. Place the image where you want it to start and create a position keyframe. Then move down the timeline and create another keyfreame. Then move the image to where you want it to stop. Go to where you want the movement to start again and create another keyframe. Then create one last keyframe and move the image off the screen.
I do this a LOT for logo loops. I start my image off screen to the left or right, then add a move behavior to the image to bring it to the center. After a moment, I add another move behavior and move it off the other direction. I like to set the move behavior to "ease both (in and out)" for a nice natural motion.
Easy to copy and paste for multiple images.
Two Move behaviors. One the length of the first move, one the length of the 2nd move. The space between the behaviors in the timeline will have the layer standing still. Using the Move behaviors gives you Ease IN/OUT.