Diane, first, you do need to keep those claws clipped reguarly.
Diane, your stain of choice should be a light stain to not show off any scratches if they do occur.
Now, there are two good floor sealers on the market. One is Oil Polyurethane and Water Polyurethane. I will use the abrev. poly for polyurethane in the future, OK.
OIL: oil is the oldest of all finishes and it does take a long time for the first coat and subsequent coats to dry. It does smell bad. It does collect dust in the drying process which is a bad thing. It does tend to turn the stain color a slight yellow in color.
WATER: water is new, the coats can and will dry in about two hours time and this eliminates the collection of dust. It does not smell. It does not turn the stain yellow. You can apply four coats of this to one coat of oil in their respectively drying time.
Remember, its best with all painting or staining or finishing sealing to apply many coats of light product. In other words do not slock on the stuff heavily.
I would recommend the water.
If Jim Sparks is viewing this, i am recommending Minwax Product.