Depending on how you feel, you may be anxious or eager for school to start.
To some people, "anxious" has more of a negative connotation than "eager." You're eager for school to start if you're looking forward to it. You're anxious for school to start if you feel nauseous every time you think about it.
"Anxious" comes from the same root as "anxiety." If you can remember that, you can remember that "anxious" isn't a good thing.
"Anxious" is evolving, though. The distinction between "anxious" and "eager" was much stronger in the seventeenth century. Today, many people use the words interchangeably.
- I'm eager to see my best friend again. (standard)
- I'm anxious to see the school bully. (standard)
- I'm anxious to get our new puppy. (acceptable, but sometimes disputed)