Use a synthetic varnish (varnish or polyurethane) to minimize absorption into the paper.
Apply multiple light coasts by spray. Paper is too fragile to handle volume applied by brush.
Glue the paper floor in place and let the glue dry before varnishing. Protect surrounding surfaces from overspray with newspaper and tape.
The choice of gloss, satin or matte is really a matter of preference. A few coasts of matte will not change the paper’s appearance noticeable. The more coasts of gloss you apply the shinier the result will be.
Any craft, home improvement, or hardware store will offer good options. Using acid free products on miniatures is always advisable.