Random orbital floor sander with rectangular base
Unless you plan to sand many floors in your lifetime, the best choice for do-it-yourself floor refinishing is the random orbital sander. Sure, it may take longer to remove old finishes than it would with a drum sander, but you don't need a lot of experience to operate a random orbital sander and most importantly, it's less likely to permanently damage your floor by causing grooves or valleys that are impossible to fix.
I have found that Clarke-American random orbital sanders are the easiest to use of the models available for rental at most home centers. In my opinion, the U-Sand is far more difficult to control, and because its sanding surface is relatively compact, it can take longer to do the job. Making matters worse, four-disk units like the U-Sand offer little or no padding under the disks, so the abrasive does not lie flush to the floor, further reducing the available sanding area while slowing down the process even more.
Pads attach to the sander base
Just because you've rented a random orbital machine doesn't mean there's no need to be careful. Be sure the sander is running at full speed when you lower it to the floor. It is also important not to move the sander too quickly across the boards. Above all, remember to never turn the machine off while it is resting on the floor. For any of these different mistakes, the consequence is the same: circular scratches on the floor surface. They may not be very noticeable as you're sanding, but they'll definitely show up when you apply the finish.
For a primer on using random orbital sanders, view our slideshow The Best DIY Floor Sander