UVs, eh? Fun stuff. First of all, what are those faces on the UV that have little notches leading in to squres? Is the entire model one piece and you cut the sides up to extrude the arms and legs out of them? Don't do that. Since the body is really just a cube and there's no reason for a smooth transition between body and limbs, there's nothing wrong with having the arms and legs be their own meshes. Like, just have a cube for the body, then create a new cube, reshape it into an arm and put it there by the side. That way you'll save a lot of polygons, and the UV will be a bit neater, too.
As for the UV itself, you don't want square UVs. Yours fit the shape of the object, and that's the most important thing. If the shapes don't match, the pixels will end up stretched and wonky when applying the texture to the object. One thing you could (and should) do, however, is overlapping UVs. Just have both arms share the same UV space, and both the legs as well. I doubt you're going to have a completely asymmetrical texture, so just make the UVs overlap. That way you can use the same texture space in multiple places on the character. You could also have both the sides of the body, and maybe even the bottom and top and back, all use the same one square in the texture space. That depends on how much light information you're going to paint into the texture, of course, and how you go about doing that.
Other than that, I can't say much right now. Just one tip for the eyes: The highlight on the iris should be on the bottom, not the top. While the eye itself is round, and extrudes outward, the iris actually goes inward, so the lighter bit should be at the bottom. It usually looks good to have the iris be shaded that way, then put a strong white highlight near the top, as well, to suggest the shape of the actual eyeball.