Simple First Game Development Ideas

I've always wanted to start creating my own games, but I haven't written any actual games since I was in grade school/high school (if you could call them games). Starting in the fourth grade, I began writing some BASIC interactive fiction type games. I haven't attempted to create anything since those days of basic "choose your path" adventure.

I just ordered a book, Beginning C++ Game Programming, that I saw recommended somewhere online, maybe Gamasutra, or GameDev.net, I forget which. So, while I'm waiting for this book to arrive, I've been thinking about the type of game I'd like to make. Not my ideal type of game, but something just for starters. I trying writing a Tic Tac Toe game in Java not too long ago, but got hung up trying to understand how to use a search tree to choose the next best move for the computer to make. I refused to use the brute force approach since Tic Tac Toe is so simple, it's easy to determine the next best move. But I was determined to learn the proper way of doing it. So I got discouraged and gave up for a while.

Now, I've freed up some time and have ordered this book to try to get me started. And I wanted to start learning C++ too, so I can kill two birds with one stone, hopefully. Anyway, I'm not thinking of ideas for small simple games I can start out with. I have some more ambitious ideas, but since I know nothing of 3d math or programming and no artistic ability, I have to stay away from the larger scale game ideas I have. So I've been thinking of maybe making a remake of Asteroids, or Space Invaders. Just to see if I can get the concept of game programming down. It's very different from server side business application programming, that's for sure.

Anyone familiar with this book I ordered (should arrive today)? Any other book or online resource suggestions you might have to get me up to speed on the basics of game programming? I need to start small and with good explanations.