Hello,
I see you are planning a web-based pathfinding project, inplemented on an already existing webserver infrastructure.
For your problem I'd suggest using either Djikstra's algorithm, for simplicity, or A* algorithm for maximum performance (although on such relatively small scale of one building, performance shouldn't matter).
The implementation I'm thinking of would send POST-requests to your webserver, allowing you to implement the database part in the way that makes most sense for your setup.
The pathfinding will then be done on the client device via optimised JavaScript. I understand you're developing this for a school building, so there will be peek usage times, and offloading the calculations to user devices will help keeping your server responsive in these.
Your database would store your building as a network, with nodes for intersections and start/end points, identifiers for end-points and the floor level they are on. Edges need to store distance or required time to travel from node a to node b (manual entry or automated estimate), their floor, and identifiers if they are represent stair or elevator (or none of both).
After picking start and end point (from a list of some kind; dropdown or similar?), the script would first request those end points from your server, check on which floors they are located, and then request all nodes and edges on these respective floors to do the pathfinding.
Please feel free to contact me if you feel my offer meets your needs.