What is standard colour of squares or lines printing on paper/notebook?
You can use Cyan or Black or any pure cmyk (not a mix of cmyk), it should be the same price. You can choose a Pantones too if you want something like green, the cost shouldn't be a lot more.
No there isn't really "a" standard, some lines use a light blue, some are dark blue like your sample. It's up to you. But if you want to get close to the most common color for this, you can use 35-40% of Cyan only. (example below.)
If you do the design yourself, don't make the lines too thin or they won't look super sharp because of the angle of the cyan on the plate; you should even tell this detail to your printer so he changes the angle if necessary, probably to black.
Example of result you don't want if you make lines in 1-color CMYK not at 100% (middle part):
(what I mean by the angle in case I'm being confusing: http://the-print-guide.blogspot.ca/2009/05/halftone-screen-angles.html)
I guess your lines should be around 0.75pts thick but you can have them thicker too if you prefer.
If you use a Pantone you don't need to worry about the angle, and you can use your color at 100%!