need to set up a second router some 50 feet away from base router/modem. plan on putting in ethernet cable, do I need to register the second router, and also how should I connect the two?

This is a small classroom that might have as many as 20 users. The first router will service the office with staff. these are portable buildings with  metal frames, so I suspect that there will be signal degradation from inside the buildings.

You're right.  Students and staff should have separate routers.

How much do you want to spend?  Would you share a printer or storage-drive off the router(s)?  Who is supplying the devices?  What cards do the device have?  Hmm...I can't think of much more now.  I think I got the main considerations.

At most $250 for the router, less if possible.

This is COX service

I can check Consumer Reports and put something together at $250 tomorrow.