For large battalions of troops I would also use GW washes.
Go ahead and base coat with black (if you must though I would use white). Hit the uniforms with a solid white, then you can blacken the rest of the mini, such as the equipment, flesh, etc and tidy those areas up. I have come to us GW Nuln Oil and it works pretty good. For your first layer you will need to go very lightly to get a bit of a greyish effect. You will need to experiment on what mixture of wash and water you need to get the look you want but I would start with at least a 50/50 mix. Don't overdue it though. Once you have an overall light greyish look you can use the Nuln Oil to add depth, such as around the straps, using a normal brush. Once again, you will need to find the right consistency so the liquid doesn't go spilling about. But Nuln Oil can be used almost like a regular paint to. Then highlight the really bright white stuff such as the straps so they pop from the uniform.
This is one of those things where you need to practice on a number of figures first until you get your technique down. Darker washes on lighter colors are more difficult to judge the final result and require a bit of skill. Once you are confident you can use the Nuln Oil without splotching it all over the mini, and using it to add depth, then you can go into mass production mode.
I think the GW washes lot quite good at adding depth to light colors. Just go easy, practice a bit first and you should be fine.
