It doesn't have to be "hardwood" stain It can be stain for any kind of wood. I've stained 3/4" red oak, with furniture stain.
The best stains are your gel, or paste stains. They have the consistency of mayonese. Hardwoods accept the stain better than say pine. Much more evenly. You also have another choice no stain at all, just natural.
Sand the floor well before finising. Use an orbital sander, on your hands and knees, use with 80 grit. The industrial drum sanders, are exceptionally hard to use, with good results,and once you screw up the surface, it's very hard to fix properly.When done sanding, vacuum, then wipe down the whole floor with damp sponge. This will raise the grain a little but, don't worry let dry. Now stain. Use an oil based polyurethane to finish. Use a paint pad on a stick. First coat light.Use a wet/dry 320 grit and wet sand do a light sanding to remove all the rough wood grain that came up through the first coat. Let dry vacuum, and damp sponge again..Now your ready for finishing coats. apply liberally (polyurethane is self leveling ) let the first coat dry at least 24 hrs. Then apply a third and final coat. Know you only asked about stain. Polyurethane is very durable, and will last long. Stay off the floor as long as you can, at least 48 hrs
Bartley makes a gel stain
google bartley stains