Self intersecting facets are a bit less of an issue than you'd think. For the most part, if there are self intersecting facets that don't break the working plane of the facets, it isn't an issue as they don't deform the mesh. Slicers look at this and just consider it mostly clean (not always, but most of the time). You have issues with this when you have facets that cross at or near perpendicular. The slicer doesn't always know what to do with them, so it either goes crazy or just doesn't slice it, leaving holes in the mesh.
A single manifold object is always the best slice. However, if you have multiple manifold objects that are close (but not intersecting) it slices OK most of the time.
The red highlights are selected facets. They are not fixed, just selected. You can attempt to delete the self intersecting facets (Delete key) then use the Fill Hole command, but that may have "interesting" consequences. Best bet is to learn where your errors are occurring and then go back and check the model in facet mode. In zBrush this may not be as easy, but then again, I don't know zBrush well.
The best pipeline is one that works for you. Your suggestion seems a bit... long, but it would help to find and avoid mesh issues. Like I said before, the best plan is to learn where your model is faulting, then fixing your modeling process so that you avoid those pitfalls. Decimate will help to clean a model up, but sometimes, you need the tri-s to make a model look good. I suggested it before because a box like that has a lot of open area and not a lot of detail. Best export for that model would have been to take it wholesale from Maya (export as an OBJ, or STL if Maya can do that) and check that in MeshLab. I would bet your tri-count would have been a lot lower. For a zBrush detail model, I'd keep it whole without decimation to get the most detail out of it.
Re-orientation in netfabb works, but I think that if you're going to produce objects for printer output, I'd download either ReplicatorG or RepetierHost to install on your machine as these will allow you to re-orient in real time, and then re-save the STL in the new orientation. Essentially, you should probably have a machine capable of 3d printing even if you don't have a printer. This would allow you to output some pretty awesome stuff (if that spider is any indication of your modeling skills). Look up posts by ysb as he's the resident guru on high quality figure models.