Went to Home Depot yesterday and see they have two sanders for rent.
One is a belt sander and the other is a large orbital. Both are
intended for floors. I just need to take the varnish off an old floor.
Is the big orbital the best tool for this? The room is 15x20ft. Any
idea how long this will take me or suggestions on the grit to begin
with? Thanks.

I rented the orbital at HD a year ago, and was satisfied with the results.
Expect to spend a lot of sandpaper, much more than the cost of the rental.
But the outcome was nice.

One nice thing about the orbital is that it has a dust bag. While the
dust bag itself is useless, if you remove it and hook up a shop vac to the
port, your sanding is virtually dustless. I don;t think we spent more than
10 minutes cleaning up afterwards.