I use a different scale for my planes, and probably the fiddliest thing I can get away with is the 2mm thick struts on the biplane. (Size comparison photo attached) If you want to make item icons like mine but at 1mm per pixel, you may have problems. The minimum thickness of sandstone is 2mm, which is partly why I chose this scale. You could maybe do something clever by rounding off the edges though.
I used SketchUp (free pro trial, I think technically you can't use the free version for commercial use). If you do you use Sketchup and want to make icons, I would recommend creating a flat plane with your icon sheet and then drawing around them with grid snapping on. Then if you fill the rest of the sheet in black, you can normally just extrude the whole thing and have most of the edges automatically be black. Depends on the icons your using as to whether you want that effect I guess.
Beyond that, most of my problems have been with the printing process on Shapeways' end, but they are seriously helpful and if you tell them about what went wrong, they'll reprint it and send you a new one.
Let me know if you have any more questions!