Clean it (Degritter Mk II, DW only), give it a fresh inner sleeve and a 5mil outer sleeve (for single/gatefold LPs), then I play it, and within a few days I catalog it.
What is the first thing you do when you unwrap a new vinyl record?
That is, apart from kiss the person who gave it to you!
You might play it, catalog it, archive it, clean it or simply store it. I am sure there are many other things you do!