Stain colors the wood, it has nothing to do with the finish(shine), and does nothing when applied over the existing finish. If you have scratches, you probably should have the floors sanded, then refinish, with or without stain. If you plan this as a DIY project, do not use a drum sander if you have never used one before. You can ruin the floors in a heartbeat. Home and rental stores have more user friendly disc sanders for redoing floors.
You may be able to perk up the old floors with a good cleaning, with stuff made for cleaning wood floors, not soap/water. Then a light coat of wax.
You may be able to perk up the old floors with a good cleaning, with stuff made for cleaning wood floors, not soap/water. Then a light coat of wax.