What are good games to "earn your wings" with?
Easy game since you don't have much state to worry about (it's an array of brick values -- if you only have one brick color, it's an array of flags), there isn't any AI, and you get to do a little bit of physics to get the ball to bounce correctly.
The rules are a bit more complex than Breakout and the interface to it is a lot different. It forces you to think about different methods of implementing a game. i.e, what works in one game isn't necessarily what you would use in another.
This one is nice because you get to work on a little bit of AI. Having the ghosts follow the player (but not too well - you want the player to have a chance) can be quickly implemented, and you will have a fun little game that you can tweak and show off to friends and family (positive feedback is always a good thing when you are starting out).
I find that if you look for inspiration in early video games, you can find tons of ideas that are relatively simple to implement. Plus, you can get away with super simple artwork and sounds because you're copying something so simple anyway. This allows you to focus on the basics first -- getting your game loop up and running, figuring out how to get your pixels to the screen, playing a sound, keeping score, getting the player's input into the game.
It almost really doesn't matter which game you choose first -- just make sure you pick something simple that you can get quick results with, that way you can move on the next day and make another one. And another. And another -- the more you make, the more you'll push yourself, and eventually you'll be making complex games before you know it.
You forgot about tetris: it was the second game I implemented back in hight school :)