Want to just make a game then use an already built engine like Unity, which is easy for beginners or UDK which is a bit more tricky, to some. These are 3D engines. Torque 2D for 2D games. Here are a list of engines if you want some in specific http://en.wikipedia.org/wiki/List_of_game_engines all have there pros and cons and type of game they are suited for, but can also work for different types of games. Such as, UDK is a fps engine, but it is capable of making a board game or RTS tile based game.
if you want to understand basics of how games are made then you want the low level stuff like OpenGL or DirectX are the popular ones. I personally was interested in making a game so I went straight into an engine, Unity since I was new with an engine environment. After a couple of weeks I know a lot about it and can crank out games pretty quick provided I had some assets.
Here is a simple game that was made for global game jam this past weekend. http://globalgamejam.org/2013/super-morbid I know it isn't AAA quality, but it was fun making and hey I actually made a game.