Depends on what finish you are looking for. Think about what you want your weathering and accenting to look like; should it be glossy or not? If you want the fuselage to be gloss and the weathering less glossy, I'd gloss coat it then do the weathering. If everything should be glossy, do your weathering then gloss coat everything.
Most of the pictures I've seen of them tend to be semi-gloss to flat finish. You can accomplish that finish using Future floor polish and Tamiya XF-21 Flat Base. The proportion of XF-21 to Future controls the matte of the finish. About 3 parts Future to 1 part XF-21 gives a flat finish. About 5 parts Future to 1 part XF-21 gives a semi-gloss finish.
You can spray it straight through your airbrush with no thinning at all. Spray at about 15 psi from 3 or 4 inches away. Clean your airbrush with Windex.
I'd play with the ratios on some scrap painted to match the bird to get it where I like it first.