I would reiterate what Wgiles and BZH said. The general advice is to wait to buy your pack until you have most of the rest of your gear so you know how much space you need. Depending on your other gear you might need a backpack ranging from 40L to 70L. 40L is already relatively large for a school bag, although not out of the question. In order to fit everything in a 40L bag for backpacking, however, you would need to be willing to use less traditional backpacking gear, such as tarps instead of a tent, most likely an expensive down sleeping bag/quilt to save space, minimal cook sets, dialed in clothing system, etc. Some of those things have a slightly steeper barrier to entry in terms of skills. If you decide to go that route, more power to you, but I wouldn't advise buying a pack meant for doing that until you are comfortable/have the gear that would fit in it.

You can always try craigslist for getting a cheaper backpacking bag (or a school bag for that matter) to use until you have more money as well.

If you think you'll only use it for a daybag, I think most any backpack will do, as you probably won't be carrying more than a couple of liters of water, food, and odds and ends. I think the difference really comes when you're carrying shelter, sleeping bag etc.