You can only use one AppleID at a time for any service. Messages, photos and such sync via your iCloud account which is tied to an AppleID. If you try signing in and out of two iCloud accounts without erasing the device each time, your going to find the data from the two accounts will become mixed between them.
You can use a separate AppleID for iCloud and a different one for iMessage, FaceTime, the music, App and book stores. But you can only change the AppleID in the store fronts once every 90 days.
And do you even know if you even can sign out of the Schools AppleID? Odds are if they assigned the AppleID for the device for school, it is under an education managed deployment profile. Typically, such profiles will prohibit your ability to use any personal AppleID with the device. That is the very point of managed device deployments. The administrator of the deployment controls what ID is used on your device, not you.