Hello- I know this is kind of late, but I work with a high end professional floor crew.
We have never used a belt sander for anything. Not even decks. As to your question about a orbit sander being enough… well maybe. It depends on how damaged the floors are. If they are uneven, warped, or heavily scratched, then I wouldn’t try it. Also depends on how difficult the finish comes up. If you plan on staining, definitely not.
If we were to do it, we’d use a ‘drum sander’ (think of it as a 150lb belt sander on wheels) to do the middle of the floor. Then use an ‘edger’ (think of them as 50lb orbit sanders on steroids) for the edges. And repeat the process a couple times with finer grits of paper. Finally going over the whole thing with random orbits to remove any marks left by the larger sanders. (On a larger room we’d only go over the edges with orbits, then screen the whole thing.)
Do to the small size of the room, you could probably edge the whole thing and skip the drum. But you’d still have to go over everything with a random orbit.
While you can rent this equipment, there is a good degree of skill required to not damage a floor. (I worked with this crew for 2 years and I still haven’t gotten to use the drum sander.)
For your size project, I’d say we’d charge a minimum of $250 for 3 coats. Getting anyone to refinish a floor for $1/foot is a pipe dream unless they are your best-good-friend. To buff/coat, maybe but probably not. And the smaller the area to be sanded, generally the more we charge per foot. (Driving to/from job, unloading/reloading equipment all have to be done regardless of job size.)