Reason for applying checkers is to see how the UV mpa is layed out on the actual model. With a checker you can see where there will be a lot of stretching in the texture.
So basicly you dont HAVE to apply the checker texture, since its only a visual help for yourself.
Now, for coloring each part of the model, is also a help for you to figure out what parts of the model needs what kind of projection mapping.
I always color my models so that it will fit as good as possible to a planer map. When all the parts are planar mapped, I go to the UV editor and clean up the UVs, so theres no overlapping UVs.
When all the UVs are non-overlapping, I start to sew teh pieces together, as good as possible trying to avoid too much stretching of the UVs.
In some cases I use cylindrcal projection maps, but only rarely, since its easier to use planars when it comes to the cleanup of the UVs.
Then when you have the model UV mapped in one or as few pieces as possible, then you apply 1 single shader to it all and export the UV map as an image start painting your textures in Photoshop or in a 3D paint software - or even both
You will probarbly have to paint lots of different textures for the same model, like color map, specular, reflection, translucency, glow etc. You name it.
In Maya you then import those files, and connect them in a Shader network of your preference.
As always, you do a shitload of test renderings.
So That is basicly what is done when texturing.
I hope this helps you.
Senior 3D Artist,
Maya Software Manager & Maya Instructor
LEGO Systems A/S