The best thing for you is to start with DarkBasicPro, for the following reasons:
- it is free (download the free version)
- it is a more stable product since it has been out for many years.
- it features both 2D and 3D, so you can do both 2D games, platforms, puzzles, etc, and you can taste the flavour of 3D programming because it has got a full featured 3D engine.
- programming is very similar to AppGameKit, so if you learn Dark Basic, learning AppGameKit will be nuts.
- there are 2 very good books from Digital Skills that teach you step-by-step how to program and the basic concepts of game programming.
- The con is that is based on Windows and DirectX, so no iOS o iGadget, sorry.
Pls go to my site to see some screenshot of games I have developed since 2010
http://darkbasicgames.altervista.org/
You can also download some little game or some demo. Of course I do not want to sell anything to you, it is only to have an idea of what can be done.
Consider that I have many years of experience in programming games for hobby. So creating the games you shall see in the site requires months of works, programming skill, passion and a lot of experience.
Anyway by installing DarkBasicProFree
http://www.thegamecreators.com/?id=2000&m=view_product&page=free
and following step-by-step the books of Alistair
http://www.digital-skills.co.uk/darkbasicoverview.html
I guarantee that you shall learn how to program in a short time. And you will be able to transfer some of your skill to your people.
Please give us back a feedback of your experience...and good luck!