Contingency names and suggestions.
Confirmed that the free-hand idea is has an actual choice impact. No extra rules necessary.
@
JeremyECrawford
You get a free interaction with an object during either your move or your action (PH, 190). You choose which.
(i.e. not your reactions)
Press the Attack
When an ally makes a weapon attack against an enemy within 5’ of you, as a reaction you can let the ally make an additional attack against the target as a bonus action.
If you have 1 hand free, and their attack hits, it deals an extra 1d6 damage.
If you have 2 hands freee, and their attack hits, it deals an extra 1d12 damage.
Counter Arrow
When an enemy makes an ranged attack or casts ranged spell against an creature within 30' of you, and you are wielding a ranged weapon, you can use your reaction to shoot the attack out of the air.
Reduce the attack's damage by 1d8. If this reduces the damage to 0, the attack misses.
Explosive Dive
When you are targed by Area of Effect, you can move up to half your speed, potentially escaping the zone. You are prone after this movement.
If you have 1 hand free, you can move 1 willing creature you can reach with you. They are also prone after this movement.
If you have 2 hands free, you can move 2 willing creatures you can reach with you. They are also prone after this movement.
First Aid:
When an ally takes damage, and you have a healing kit and a free hand, you quickly run over and slap on a bandage before their insides become outsides. They can spend half their maximum hit dice (or any remaining if they have less than half), and immediately regain those hit points. If the target was reduced to 0 HP, they do not fall down.
If you have 2 free hands, you can maximize the hit die roll.
Adjust Movement
When an creature within 5' moves, you either give them a friendly shove to increase their movement by 5', or hamper them to reduce their movement by 5'.
If you have 1 hand free, increase it to 10'
If you have 2 hands free, increase it to 15'.
Reposition
When a creature within 10’ moves, as a reaction you may also move, up to your normal Movement rate. The distance you move is deducted from your movement on your next turn.
If you have 1 hand free, increase the triggering range to 20'
If you have 2 hands free, increase the triggering range to 30'.
Bait and Switch
When an enemy makes an Attack of Opportunity against you, as a reaction you may lure that enemy into overextending itself. It provokes an oppertunity attack form each other creature within 5' of it except you.
If you have 2 hands freee, your allies attacks have advantage.
Bolster Resolve
When an ally within 10’ fails a Wisdom Saving Throw, as a reaction you can allow them to re-roll it. You must be able to speak and the ally must be able to hear you.
If you have 1 hand free, increase the triggering range to 20'
If you have 2 hands free, increase the triggering range to 30'.
Adjust Reaction
When a creature within 5’ is the target of a spell that requires a Dexterity Saving Throw, you may use your reaction to either grant Advantage or impose Disadvantage on the saving throw.
Skirmish
When an ally provokes an Attack of Opportunity from an enemy within 5’, use you reaction to prevent the attack.
If you have 1 hand free, increase the triggering range to 10'
If you have 2 hands free, increase the triggering range to 15'.
When you are the target of a weapon or spell attack from an enemy within 5’, you may use a reaction to impose Disadvantage on the attack.
Protection fighting style is already a thing.
When an ally makes a weapon attack against an enemy within 5’ of you, as a reaction you can take the Help action, giving that ally Advantage on the attack.
IMO, everyone should get help-as-reaction, that works for both skills and attacks. It's generic enough so players will always have at least 1 option even if they picked all bad contingencies.
And trading out contingencies is 1/level.