I think modding is a good place to start for game design. It allows you to make a game (although with a lot of limitations) without all the work and gives you a look at how the game was made. I think one of the best games for beginners to mod is Warcraft 3. It is where I got started. It has an easy to use map editor, an object editor, and uses both drag and drop scripting and classic scripting with it's custom language Jazz. Skilled users have created RPG's, FPS's, and even a roller coaster simulator. I've heard Starcraft 2 is has more features but I've never played it. Other good games to mod are Half-Life 2 and Civilization 4. Civ 4 can be easily modded with XML or you can get even more power using Python.
For programming I started with BASIC. Don't do that. It is an extremely messy and outdated language. Modern dialects might be better but, I have not tried them. After a few weeks with BASIC, I switched to Python. I would recommend Python because it is easy to learn, write, and read. Another good thing is that many programs use it for scripting, such as Blender (which has a game engine) and also, many libraries have bindings in it. What doesn't have a Python binding will have it in C/C++ which could be included into a python program with ctypes. A good thing with C/C++ is that so many programs are written with them and most libraries have bindings in it. Another thing is that many languages are inspired by it.
With programming you should get inspiration. You could read open source programs' code (start small). A lot of important and advanced software is open source. The DOOM engine, SCUMM, and even the more recent id tech 4, are now open source. You can even find the source for Valve Software products at their GitHub page. Just don't copy anything they have because it is not FOSS.