The purer the sand (i.e., the higher the silica concentration and less iron) the better, as it is the other impurities - desired or undesired - that give glass its color.
Low iron means more control over the ultimate color (Hunter 1950; Tooley 1953).
Glass chemistry is a complex science that is beyond the goals of this website and will not be pursued here.
For one who wishes to pursue this subject, Tooley's (editor & one of the chapter authors) 1953 book "Hand Book of Glass Manufacture Volume 1 - A book of reference for the plant executive, technologist and engineer" is recommended though possibly hard to find.
Glass which is composed of pure silica (99.9% ) would be colorless glass.
However, making glass from pure silica is not practical or commercially viable because of the prohibitive expense of acquiring such in its pure state and the much higher temperatures needed to properly melt.
This is done by adding certain types of compounds to the glass batch in certain quantities.
Bottles made from glass with just the basic ingredients (sand, soda & lime) will usually be different shades of green because of the iron impurities in the sand, though other colors can also be attained depending on many factors.
Although classification by colour is simple to do, the end result is of little value for the following reasons: colour does not have a direct relation with glass type (the common green, amber, and brown glass colours can occur in soda, potash, and lime glasses; many lead glasses are coloured); colour is not related to the technology of glass object production (i.e., it has nothing to do with whether the glass is free blown, mould blown, pressed, or machine made); colour is only weakly related to the function of the object (almost all colours can be found in all types of objects, an obvious exception being "black" glass which does not occur in tableware).
Given these factors there is little justification for using colour as a means of classification.
With higher amounts of iron or higher oxidation of the iron, darker greens will usually occur (Toulouse 1969a; Jones & Sullivan 1989)).
In order to create other colors, the iron needs to be variably neutralized and appropriate colorizing agents or compounds added to achieve the desired color.
Glass composition formulas were (and probably still are) closely held glassmaker secrets as the experience of extensive trial and error experimentation in glass making was not readily shared with others.