code structure / program design tutorials?

Check the "Resources" link at the top. You'll find lots of what you want in there. Particular the Game Programming section. Most people will probably refer you to the Engineuity Article.

"Engine" development is a rather complex issue and there isn't any perfect solution. Like many things, there's pros and cons for different approaches. It also depends on the game you want to develop. A 3D first-person game has different demands than a 2D platform adventure. Even the adventure game needs much more than a puzzle game, for example. Different styles of games often require different engine solutions, so an easy answer to your question is not possible.

After reading tutorials and whatnot, what you should probably do is pick a graphics API to work with (OpenGL, DirectX, SDL, whatever) and just dink around with that. That will instantly teach you a few core game programming concepts (mainly, the need for a "game loop", object processing, and rendering). If you do this, the issue of what classes you need will be answered organically. You'll have a need for something and then start to add it when you do. It's not like you have to have everything all at once!

Software architecture tends to be more of an art than a science. Design patterns books/resources might help, but in the end experience is the best teacher here. Make a few 'throw away' apps/tech demos/games and see what works and what doesn't.