These apps are completely different animals. If you are going to produce training videos that are more than a few seconds long then you need and editing program like Premiere Pro to edit the shots and do the sound and music mixing. After Effects or something like Cartoon Smart can be used to create the cartoons. Premiere Pro will take you about a week to get a handle on, After Effects will take quite a bit longer. If you have not done any cartoon animation before then you either have to know how to draw and understand the principals of cell animation or use something like Cartoon Smart to create your characters. Edge Animate and Flash are for creating interactive animations not for making movies. You can embed movies in either and both have long and steep learning curves to do something like you are describing.
Photoshop if for editing photographs and if you are a skilled artist you can use it for creating original artwork from scratch. Illustrator is probably better suited to create cartoons. There is no program that you can just buy and a week later produce a commercial product. The hardest part of training videos is not the animation, it's the writing. Most online training is really awful because of poor writing so that's where you should start. Either learn to write training or hire or collaborate with a good writer, figure out a style that you want to emulate, make it your own, learn the appropriate software, make a good demo, then go out and pitch your work. The last training videos that I worked on that were mostly animation had a production team of 15 people and we worked for a month to produce 5 hours of quality training. About 750 man hours were spent on the project. Cartoons are not fast and easy. There are no magic buttons you can press to make things work out in minutes.
If you give us an example that shows exactly the kind of thing you want to do then we can give you an idea of production techniques to achieve your goal, production time per finished minute, and the amount of time you can expect to spend learning how to use the software to create the product.