Once happy with detailing, now comes the texturing part. I love it and always been beaten up by mom for messing up my home walls. Also I can't stress on how much real life references are useful for texturing. Always refer to real life objects, their surfaces and how they react to light and environment.
So as Uvs are already laid out properly, I apply shader and start painting in Photoshop part by part. I hand painted all the textures from scratch in Photoshop. Started with the base color, made some custom brushes to add layers of dirt and weathering on objects. Then desaturated the color map and tweaked it to be used as bump and specular maps. Try not to paint too much of darker and highlights in color map, and let the light do that. Pay attention to finer details.