1080p is 1920 x 1080 at 30 frames per sec (rounded off), 720p is 1280 x 720 @ 60 frames/sec.
The TV networks ABC, FOX, ESPN and A&E use only 720p/60. Most others use 1080/30. So both 1080/30 and 720p/60 are truly HD and both part of the ATSC HD standard.
1080p/30 gives higher static resolution but lower temporal resolution. At certain rates of camera or subject motion, the effective resolution of 1080p/30 will drop below 720p/60.
In general I'd suggest using 1080p/30, and create the Premiere Project for that resolution and frame rate. For brief slow motion sequences use 720p/60, which plays smoothly at 1/2 speed. You can drop 720p material into a Premiere 1080p project. You can intercut between the two types although each 720p clip will require upscaling, else it will look slightly window boxed.
On many DSLR cameras aliasing (the stair-step jaggy effect on straight lines) is worse at 720p, so that's another reason to prefer 1080p unless otherwise needed.
Once the project is finished you can render the output at whatever resolution you want. E.g, for Youtube H.264 at 720p/30 is much more time and space efficient than 1080p/30.
For playing the video in a classroom you can render an MP4 file at 1080p/30 and play from a laptop or other device. However at the typical classroom viewing distance it's unlikely they could see the difference between 720p and 1080p, or maybe not even DVD at 480p.
If you have Premiere Pro and ability to burn a Blu-Ray and the classroom has a player you can burn a Blu-Ray disc.