It’s a good idea to start with a simple 2D sprite game, as you’re doing, because game programming is some of the most difficult programming you can do. It takes a great deal of time and study, as you note. Doing 2D will help you learn how to deal with frame rates and rendering, then you can take the plunge into the much more difficult world of 3D, if that’s your intent.
In my experience the real work in doing graphics is knowing math. I mean heavy math. Lots of it. For example, geometry, trigonometry, linear algebra, algebra, calculus, etc. In fact, if you have a degree in math, you’d have a big edge in doing graphics programming, especially 3D programming.
Here are some websites:
The best website was www.flipcode.com. Sadly, the site is now dead, but some of their forum archives are still there, so you might want to try them. The guy who ran flipcode recommends http://www.devmaster.net/ as a replacement.
Another great site is http://www.gamasutra.com . Here you’ll find papers, video lectures, and even job postings.
http://www.gamedev.net this has papers, forums and general information.
For DirectX these sites are useful:
http://www.32bits.co.uk/ This was my favorite site for learning DX.
http://www.andypike.com/tutorials/directx8/
http://www.riaz.de/tutorials/d3d.html
For OpenGL:
http://nehe.gamedev.net/ NeHe’s site is very popular, and great for beginners to OpenGL. He even puts on contests, which are great fun, because you can see some great work done by amateurs.
http://www.opengl.org – check out their forum for questions you might have.
For Hardware (graphics cards):
http://www.beyond3d.com/
http://www.tomshardware.com/index.html
Both of the above are excellent.
Books:
There are too many to mention them all. Here are some.
Computer Graphics: Principles and Practices by Foley, van Damn, Feiner, Hughes – this is the bible on the subject. Although it won’t get you directly to writing a game, since it’s lots of theory.
The Graphics Gems series by Glassner, is expensive, but full of gems, as the title says. I only have one of these books, but everyone tells me that they are worth getting if you’re a serious graphics professional.
OpenGL Game Programming by Hawkins and Astle
Intro to 3D Game Programming with DirectX 9.0 by Fank D. Luna
I don’t have any book on 2D graphics per say, but I’m sure you can do a search on the web for such a book, or ask around.
Anyway, there is some information for you. Those leads should help you find your way. Ask questions of the guys on the forums, because there are some very knowledgeable experts out there.