Since at some point this will be my problem with my 15 mm Star Wars figures and looking at the last couple of responses, I think I'd go with whatever is your preferred primer color, then paint as carefully as possible - but understanding there will be 'spillage' - the inner black portions. Then paint the white portions, and then the black portions that can't be done effectively until after the white. Shoulders pads and other varied colors after any highlighting (dry brushing in my case). Where the white is covering any spillage where it isn't full coverage for any reason (should be pretty good coverage mostly) I'll just think of it as part of the 'weathering' of the figure though I think the dry brushing will minimize it.
Sort of the paint from the skin outward technique of layer painting. Not sure in 15 mm I'd attempt those thin lines on the legs, probably use a wash technique to get some of the detail with dry brushing layered above.