Elemental Origin:
At 1st level, select how you gained your elemental powers. Your choices are Mage (via Study), Blood (via ancestry), or Artifact (via exposure to an artifact charged with elemental energy).
This choice modifies how you express your elemental magic.
Elemental Alignment:
At 1st level, select which element you are aligned to. Your choices are Fire, Water, Earth and Air. These align with the damage types Fire, Cold, Thunder and Lightning. Your Elemental Bolt and other powers will refer to this damage type.
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Elemental Defences
At 1st level you can use elements to bolster your defences. When not wearing armor, or using a shield, you can do one of the following, as determined by your Elemental Alignment:
Fire: As a reaction when hit by an attack you can blast your attacker with fire. They must make a Dex save, and on failure, you deal Elemental Bolt damage and the attacker must reroll their attack. You can use this once, plus once per 2 elementalist levels, between short or long rests.
Earth: You can harden your flesh. After a long rest, or as an Action, you can gain 4 plus twice your Elementalist level in temporary HP. If you use this ability as an Action, until the end of your next turn you have Resistance to all damage, Advantage on Con and Str saving throws, and attacks on you have disadvantage.
Air: The very wind protects you. You may choose to calculate your AC as 10 + Intelligence Bonus + Dexterity Bonus. In addition, as a bonus action you can create a ward of wind in an empty hand; until you use the hand for something else, you gain a +2 AC bonus.
Water: When you are wounded, your control over water lets you patch up your wounds. When you take damage, you can gain temporary HP equal to half of the damage you took. You can do this once, plus another time for every 2 elementalist levels, between short or long rests.
Design Notes: These are intended to give the character flavourful defences.
Fire is pyrrhic defence. Earth is a pseudo-dodge action that pseudo-buffs your HP from a d6 to a d10. Air is classic "unarmored AC" with a pseudo-shield. Water is a bit like the Rogue's uncanny dodge, but it doesn't use reactions, and it only protects you from the next attack.
The "Artifact" origin would be the melee gish, and would have a Int+Con AC calculator, but wouldn't have the ward.
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Shaped Escalation
Starting at level 3 as an Elementalist Mage you can shape your escalations. As an action you can consume a use of Elemental Escalation in order to do one of the following effects, as determined by your Elemental Alignment:
Fire: Select a point within Elemental Bolt range. An explosion of fire occurs there. All creatures in a 10' radius sphere must make a Dex save or take your Elemental Bolt plus Escalation fire damage, save for half damage. In addition, unattened flammable objects ignite.
Water: Select up to 2 targets within Elemental Bolt range. An icicle flies from your hand and attempts to pierce them. Each target must make a Dex save or take Elemental Bolt plus Escalation cold damage, and on a successful save takes half damage
Air: Select a target; they are surrouned by a small Tornado. They must make a Str save or take Elemental Bolt plus Escalation lightning damage and be lifted 10' into the air until the end of your next turn, at which point they are lowered 10' and then dropped. While lifted in the air, their speed is reduced to 0, their attacks and Dex saving throws are at disadvantage, and all attacks on them are at advantage. If they succeed on the Str save, they are not lifted, and they take half damage.
Earth: You create a Shockwave that is 5' wide and as long as your Elemental Bolt range projecting out from your hand. All creatures in the Shockwave must make a Str save or take Elemental Bolt plus Escalation Thunder damage and be pushed 10' back and knocked prone. On a successful save, they take half damage and are not pushed or nocked prone.
(I think Water is lackluster; I revised it below)