I have a bunch of videos and pictures. I want to make a compilation with them. I just don't want it to be worse than movie maker. I am looking for these moving effects that you can play while the video is changing ( http://prntscr.com/29coci ) I already have experience in After Effects and Photoshop CC
Premiere Pro has a number of default transitions under the "video transitions" tab in the effects pane (usually located in the bottom left of the window). Are those what you are looking for? If you have experience with After Effects, you could also use AE's more robust effects library to animate interesting effects for your videos.
Based on your included image, it looks like you might be interested in wipe transitions.