With that in mind, here is the process I have come up with. It is fairly fast, and gets pretty good results. The unit I tested this method out on was a unit of 25 Mantic Games Skeleton Warriors. All the paints I used are from a prior set of Citadel Paints, so the names are not the same in their current paint line. However, there are probably equivalent colors that just have different names now.
I first prime the models black, then start out by painting all the bases Calthan Brown. Then I drybrush the bone and cloth areas with Dheneb Stone. I don't worry about getting it anywhere else, just make sure to get the bones and cloth. The main reason for this is to make the paint go on easier in subsequent steps, so that none of the colors will require multiple coats.
Paint all the bones with Skull White, leaving black in the recesses.
Paint all the cloth with a base color, in this case Iyanden Darksun to give them yellow uniforms. Leaving black in any recesses should be fine here, too, but for the most part it was easier not to. You also want to be careful not to get any on the bones. Drybrushing a lighter color on the cloth areas here might improve the result, but I didn't there. I may try that out and see if the result seems worth the time it takes.
Paint all the wood parts and leather straps with Graveyard Earth. You could use a different color for wood than for leather if you want, but I didn't find that it made much difference.
Paint all the metal parts with Tin Bitz.
Here I stippled Vile Green on the metal areas that I wanted to be ancient, aged bronze. Jade Green can also be used, or a combination of the two. Here I just used Vile Green. If you want steel weapons, skip this step.
Drybrush Dwarf Bronze on the Bronze metal areas. For iron or steel, drybrush Boltgun Metal. I did this in two passes, getting the large areas first, then doing a second pass with a smaller brush to get the small or hard to reach areas. This way I could get it all without getting too much of the paint on other areas where it didn't belong. Actually, I used a similar two-pass method for doing several of these steps, so I could do the large areas quickly in the first pass, and fill in smaller details in the second without messing up areas I had already finished by using too large of a brush.
Wash Devlan Mud over the cloth, wood, and leather. Try to avoid the bones and metal as much as possible. If the cloth was some other color, this might need to be two steps, with a brown wash on the wood and leather, and some other color over the cloth. But Devlan Mud seems to work well for shading a wide range of base colors, so it might work for most cloth colors.
Wash Badab Black over the bones. After this dries, you could do a quick drybrush of Skull White again over the most prominent areas of bone, like the faces and hands, to lighten them back up a bit. This takes very little time and I think improves the result, so I find it worth doing. You can do the same with some of the cloth areas that are most prominent if you want, though I didn't.
I think the results look pretty good, and the method is pretty fast, but it could probably be improved upon. Please let me know if you have suggestions on how to improve this method, either by getting a better result without adding much time, or by reducing the amount of time it takes while getting a similar result. Obviously you can save a step if you don't want the weapons to be Bronze, but I really like the aged bronze look, so I thought it was worth the extra time. Let me know what you think.