I would think that since you floors are level, the vibrating or orbital sander would do a very good job, the drum does take off allot of surface if your not careful.
Orbitals do get up close to the baseboards or walls also. Be sure to use the grit paper pattern correctly.
Also, be very concerned and intuned to dust pickup. This stuff will haunt you when you begin the staining and sealing. Dust is the culprit of many floor restorers. Take all the precautions to remove all of it from the job site.