It's difficult to definitively say which three non-metallic minerals are the "most important" as their importance depends on the context and criteria used for evaluation. However, here are three non-metallic minerals that are incredibly important and have widespread applications:

1. Quartz (SiO2): This is arguably the most important non-metallic mineral. It's a major component of glass, ceramics, and electronics (for its piezoelectric properties). It's also used in abrasives, construction materials, and even watches (for its timing properties).

2. Feldspar (various compositions): Feldspar is a major component of many rocks, making it essential for the construction industry (as aggregate in concrete). It's also used in ceramics, glassmaking, and as a source for potassium in fertilizers.

3. Halite (NaCl): This is more commonly known as rock salt, and it's vital for its use in seasoning food, as well as its role in de-icing roads, preserving food, and producing chlorine and sodium hydroxide (important chemicals for many industries).

Other important non-metallic minerals include:

* Gypsum (CaSO4·2H2O): Used in construction materials like drywall, plaster, and cement.

* Fluorite (CaF2): Used in the production of steel, aluminum, and glass, as well as in various industrial processes.

* Diamond (C): Though often associated with jewelry, diamonds are also essential for their hardness and use in cutting tools, drilling, and polishing.

The importance of each mineral can vary depending on the specific application and industry. Therefore, it's best to consider the context and criteria when ranking the importance of non-metallic minerals.