Can I JUST stain a wood floor and not varnish it?

Sand it and seal it. Staining with an oil stain would probably give you the least work, but it's not a "put it down and come back in 25 years" situation - you'll still be refinishing it every couple of years. Maybe more frequently if that traffic is really heavy. Some kind of tough topcoats (4 or 5 very light coats) might protect it longer. It depends on what's being done to it. Clean shoes don't wear a finish as fast as minute sand or quartz particles brought in from outside. (They can sand a finish off in minutes.)