The game won't run on D, but i know people who use it... anyways...
The point is, if you learn ansi-c and then get used to C++, you'll think C++ is easier. If you learn D... you probably won't use C++ or C at all. I'm not sure what its like, but i know my friend isn't about to switch over to C++ (he uses D)
I'd have to recommend just using C++. Its the defacto gaming language. Its available on almost every platform. Its backwards compatible with C. Its really fast and efficient, and you can do almost everything anyone has ever done with software with the correct knowledge and the correct hardware. (Except for a bootloader. You wouldn't want to write one of these anyways, and you couldn't if you knew C and not assembly language because it needs to be written in assembly language even if only a little bit.)
My last comment reminds me, assembly language. You can leverage your processing power very directly with assembly language. It is harder because it requires knowledge of how the processor works. When you write assembly language, your really writing expanded machine code, which is the main part of every program on the intel x86 processor (which is most likely what your using unless your on a mac thats not intel) and that means if you could almost put it in a hex editor and use find and replace to write machine readable code (Though you have to write special data around it that would make it run in your OS, which is one of the things that an assembler can do. Oh, and its basically impossible for someone to write out a whole application that works out of the box in a hex editor - so if your interested in that use a really good assembler..)
Anyways, i do recommend C++. I did assembly a while ago when i was writing some code that needed to be used to boot up a program on my PC but i now have forgotten most things i learned anyways.