You can use an orbital sander on that size of area. Sometimes, in small areas you cannot even use a belt sander. However, you must sand the entire area evenly. This is why your husband wants a belt sander.
It will take more time with a small hand sander, but that is how I would do such a small area. Make sure to sand evenly changing the paper frequently. Then, go to a finer grit paper and evenly sand again. Finish, with about 220 or finer paper.
Then, apply the type of stain you perfer.
Finish with poly. I recommend Helmsman's Spar Urthane for areas that see any foot traffic. I also recommend Satin finish. Satin finish won't shine like gloss, but it doesn't show any dust or dirt either.