Advice/Help with Support Structure

[eaturbrainz]

I've downloaded a model of an ArWing from Models Resource, and spent plenty of hours cleaning it up and making it one solid piece. The problem I'm having is generating/modifying a support structure for it. The first time I tried printing it, using Cura's support structure, I couldn't break the support away without destroying the wings. I've also played around with the support options in MeshMixer and B9C, but the print keeps boogering up lower parts (circled pink in the image). I guess my question has a few parts to it. Should I print the thing standing up or laying flat? Also if anyone has any suggestions for generating a support structure (programs, recommended settings, etc.) I'm all ears.

For some more info... I've had my 3D printer (Printrbot Simple Metal w/heated bed) for about a month now, finally got it dialed in (lots of cubes and abstract shapes later...), and this is BY FAR the most complicated thing I've tried to print. I've also designed and printed a stand for the ArWing if you wanted to know what the hole in the bottom was for.

The ArWing: ArWing.STL
The Stand: 50mm_Base.STL