Disclaimer: I'm not connected to these websites or brands even thought I use some of them. I'm offering links to good basic gear that you might find helpful. Feel free to do other research or purchase other brands, and by all means, if you can buy local, I hope you do!
Lots of different kinds of sticks out there for various music situations. A good place to start is with a 5A (thinner and a pretty light) or 5B (a thicker stick with a bit more weight). Ultimately, the sticks that feels good is the one you should use. Smaller person? 5A. Adult? 5B. Either would be fine for basic school band or drum set playing. Sticks are made from all kinds of wood. Hickory is the most common. It's durable and easy to find. Maple(a lighter wood) and Oak(heavier) are also used but don't overthink it. I would also recommend wood tips for now.
Sometimes concert band can require a special kind of sticks. There are others but these are the ones I have always used. Vic Firth SD1 General. But you are in in school band and have 5A drumsticks, you're fine.
Marching band requires a much heavier stick. Different schools and programs have certain models that will use, but these are one of the standards.