Hey there, welcome to the forums!
I love the idea of making games for family, it's very rewarding for all involved. As for the easiest way to do it, there are several considerations here. Firstly, you have mentioned that you don't have much programming experience. Most of the tools The Game Creators offer are programming-centric, and would require you to code most of the game. This can be a bit of a stumbling block to new users. Secondly, there are other, more purpose-made tools, depending on the type of game you want to make.
With your stories, would they fit the point-and-click genre, platformer, RPG, etc? There are dedicated programs available for those genres that might make developing your games easier.
Let me know what you are thinking and hopefully you can find the right tool for the job