I'd highly recommend Sand Paper ;-) Joking of course. Depending on what I'm sanding, I start with 120 grit and usually work my way up to 400. If I'm working on something that requires very smooth work, I go up to 600 grit and sometimes even 1000 grit. I use my orbital finish sander and 320 sandpaper for larger items, but it's hard to get into corners and edges with a machine.
I've used the dremel, but typically it removes too much, too fast for my tastes. I prefer hand sanding to get into the curves and sharp turns. I bought some sandpaper designed to go into a scroll saw, but have yet to try it out.
I think you will be in good shape by visiting your local home improvement store and get a package each of 120, 220, 320 and 400 grit sandpaper. Sometimes it helps to wrap the sandpaper around a dowel rod to get into curved parts.
I have projects that I sand all the way up to 24,000 grit, but these are items that will be worn or looked at incredibly close.
John