Sorry friend, but in Pathfinder these three are all the exact same character mechanically, just with a different Admixture focus.
(also you might want to lay off the chuunibyou a bit)
If you want 3 actual wizards you basically build em the same way, but if you want 3 quite different mages how about this:
Frost: Winter Witch / Winter Witch
Fire: Sorcerer / Dragon Disciple
Electricity: Magus, Arcanist or Wizard
Feat stuff is basically in the line of "Elemental Focus: ( element )" and maybe one of the elemental Meta magic feats.
These character concepts are pretty broad and could be represented in a number of ways. Most people will just suggest 'Wizard' or '9th level Arcane caster' but I'll try to take it a step further with specifics.
Obviously Arcanist, Sorcerer, and Wizard could all fit pretty well with the themes you're trying to pursue here. The air, fire, and water elemental schools would work as either a Wizard or school savant arcanist.
Sorcerer is another choice, using the elemental bloodline to good effect. Alternatively, blood arcanist could work for that purpose as well.
And finally, the arcanist alone offers the elemental master archetype.
Most blast styled spells like what you're looking for come from the evocation school, so the spell focus (evocation) and greater spell focus (evocation) for feats are good choices, and the elemental focus and greater elemental focus feats are basically no brainers.
I hope this can help you get the gears going in your head for exactly how you want to build these characters, and maybe help to show that even though the concepts are similar, they can be certainly distanced and played quite differently from one another.