Here is my view for the absolute newbie to programming:
1) Choose a language with auto-memory management as standard, which in my opinion is wise for a first time beginner, since you should only be practicing high level coding for a while.
2) Pick one of the more common languages because they have up to date support and plenty of information or help is available for them. Examples are Java, Python, Lua, C#, Pearl, Ruby, and Visual Basic.
3) If your long term goals are to use a game engine, then select one now and begin to learn the native language for it over the next several months or more before you even touch the game engine. One way of choosing a game engine is to look at the games made with engines and compare with your own goals, for example searching for Torque 3D Game in the YouTube search box. Another good way is to go to the community forums about the game engines and see what is submitted there for review.
Most game engines have the added advantages of a large community knowledge base and excellent direct support.
List of Game Engines
4) Before you make any games, learn the basics of your language of choice by following tutorials or courses on making simple console type applications (not to be confused with console games). Some examples of these types of programs are: Simple Data Base, Letter Display Application, Auto-update Index, Simple File Handling Interface, Alphabetical Indexer, and so forth. The list of simple applications is enormous, so do a little research on what to make. Don't just copy the tutorials but understand each line of coding before moving to the next. About 3 to 5 of these should be enough to get you started.
5) Create a few simple games next, such as crossword puzzle, Tic-Tac-Toe, Question and Answer Game. These can be made as console applications, but some game engines have a good 2D potential which could be used to make these.
6) After several months or more, then focus on making simple 2D games with the game engine.
7) An alternative to the game engine is to learn to make vector graphics 2D games which target a specific Runtime Environment. This allows you to avoid OpenGL and Direct3D APIs for a year or two in order to build a solid foundation in coding and not develop bad habits as readily. Some game developers really enjoy the vector programming and can even sometimes earn a living doing this, so don't underestimate the value of this. Some popular games have been console types.
8) The 3D game development genre would be next after 1-2 years with the above foundational knowledge.
Last couple pieces of advice are to choose rewarding and self-feeding paths of learning which let you see tangible results on a regular basis and also keep things within your abilities.