I do friend, I ended up looking into a few years later/have other teachers explain it but I never had that spark about it again

Huh? It's sorted by number of electrons/protons (atomic number) the mass is dependent on that and the number of neutrons.

The eight main groups are based on the number of electrons missing for the atom to reach a full valence shell. Once it is full (8th group, noble gasses) it starts a new Period (row). I'm not sure how the other groups are chosen (probably some quantum physics that I never had in chemistry class). After looking it up Wikipedia says it just keeps going that way.

Electronegativity describes how much it "wants" to attract negative charges and doesn't affect the order (Flourine has the highest and is in group 7). I think you may have confused it with ionization energy which would certainly match my understanding of the top half of the periodic table and probably does work for the lower half too now that I think about it.

The groups tend to have similar properties but that is not why they are sorted that way. Hydrogen for example is quite different from other elements in group one. The colours are probably better for finding common properties.