Recommend power sanding. Trouble with sanding round-and-round is that you cut in the same direction with the gouge and the previous grit, so you will have a long time reducing any ridging, and a nearly impossibly time reducing any proud area on an otherwise fair surface. With a sanding disk you will be cutting across the ridges, and by pausing with the proud area under the contact portion of the disk, you can regain that fair surface.
Low rpm selection is folklore, except that certain setups have a max recommended for the mandrel. Reversing direction to pick up what was laid down is also folklore. If the disk is rotating, it is sanding across the surface of a rotating work. Depending on which portion of the disk is in contact, and the differential rpm, you can decrease the angle to approximate sanding round and round, though you'll never get there. Take advantage of the inevitable and sand first with any grade close to 6:00 or 12:00 on the disk to clear ridging with the most aggressive removal. Move toward 9:00 (clockwise disk rotation as you view it) to finish each grade.
You may continue the process through any number of grits you choose, or you can realize that the human 20/20 can't really tell scratches lower than about 320 line pairs/inch if they do not make great contrast with their background. When you get done with the 320 (P400) on the disk, sand by hand, along the direction of the grain to reduce those visually high-contrast cross-grain or circular scratches by removal and blending. You can use artificial high contrast to verify your quality by shining a bright light at a low angle, accentuating any ridges against their shadow. I like to wet, then sand with the grain, wet a second time and re-sand up the grain.
Whatever you do,
DON'T PRESS as you sand. It ensures you will make the deepest grooves possible with that grit if you do. Takes longer to get them out with the next. If you sand real hard and heat the surface, you get a slick "case-hardening" to shine with your scratches as background (remember that contrast thing?) to frustrate you doubly on the next grit. Deep scratches will demand you get as deep, and a hardened surface that won't allow the next grit to bite as easily. If you have this circumstance, damp rag, make sure you have a dull and dry surface, and start from there.
Use what you have for now to spin the disks. I like my flex shaft, because I can support it on the toolrest like all the other tools, and only kiss the high spots as I work. Sort of like the folks who use scrapers fresh from the grinder, the grit only contacts the high spots until they're gone.
http://s35.photobucket.com/albums/d160/GoodOnesGone/?action=view¤t=150Sand-1.mp4 Drills work, but they're heavier since they don't rest on any support but you and the work (remember, don't press), and they are run by DC or universal motors which make more noise, heat and - are you ready dust explosion believers(?) - sparks than a nice induction run motor.