5) Go to Window -> UV Texture Editor...

This will open up your texture view.

6) Select the faces you just applied the Y-axis planar map to, and in the UV window, choose Select -> Convert Selection to UVs

7) Press "w" and move them somewhere out of the way of the rest of the hand.

While doing this, you should notice your checker texture "flow" over the model.

8) Scale your UV selection up a bit.

From here on, your main goal will be to keep a uniform checker look over the surface of your model by moving your UV's around in the UV window. Mind you, they don't have to be perfect squares, but the cleaner they are, the better. This is because when you export your UV map and paint a texture, any/all non-square sections refer to "stretching" of the texture, and WILL have that effect on your texture's appearance on your model.

That is, no matter how pretty a texture you paint, if you don't have clean UV's, your texture will look (more or less) like the the above link.

So again, you don't need absolute perfection, but the closer, the better

I'll be working on this right now, so I'll post an image when I'm done.