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The DMG (p. 249) gives some guidelines on improvising damage. It suggests that falling into a fire pit might cause 2d10 damage. In the case of someone running through a small area of fire as per your scenario, I'd look to the create bonfire cantrip from the Elemental Evil supplement: You create a bonfire on ground that you can see within range.
This small container holds flint, fire steel, and tinder (usually dry cloth soaked in light oil) used to kindle a fire. Using it to light a torch—or anything else with abundant, exposed fuel—takes an action. Lighting any other fire takes 1 minute. So here is an item that gives us our staring point.
That specifically does fire damage from an ignitable source: 1d4 fire damage per round until a DC 10 Dex save is met, which costs an Action to roll. That is potentially devastating over ten rounds dealing an average of 25 points of damage if not dealt with (which is roughly the equivalent of Fireball), and if extinguished will cost the target ...
In Tomb of Annihilation, lava does the following damage: Any creature that falls into the lava or starts its turn there takes 55 (10d10) fire damage. Any object that falls into the lava takes damage on initial contact and once per round thereafter until it is removed from the lava or destroyed.
And when applied deal an extra 5 to any fire damage within a minute. I’ll be using magic missile like crazy and changing to fire for a +11 damage to each roll and I’m thinking about a single dip into hexblade for an extra +6 eventually but let’s even it out and say it’s a +3, that’s a minimum of 15 each dart. 4 darts is 60 minimum.
At 18th level, you gain immunity to fire damage. In addition, any spell or effect you create ignores resistance to fire damage and treats immunity to fire damage as resistance to fire damage. Other options. There is the Elemental Bane spell. But that only covers resistance, requires a save and is concentration. Not a good option.
Which damage types are the most resisted, and which are the least resisted in DnD 5e? For simplicity's sake, I would limit this to monsters from official WotC sources, and would classify immunity as a form of resistance (though if an answer chooses to distinguish between resistance and immunity that would be fine).
First of all, pick a baseline damage: d6 for a low damage effect, d8 for medium damage, and d10 for high damage. If the damage can happen more than once, reduce the size of the die. So, for a continuous effect or a trap that goes off every round, the damage is d4, d6, or d8. Now decide if the damage is leveled.
Make a ranged attack against a target creature or object, treating the oil as an improvised weapon. On a hit, the target is covered in oil. If the target takes any fire damage before the oil dries (after 1 minute), the target takes an additional 5 fire damage from the burning oil.
It was a low roll as well, given that it was 12d8 Radiant Damage (Level 3 divine smite plus improved divine smite on the weapon and smite damage), 6d6+1 of magic weapon damage (I'd used a potion of Giant Size), an extra 6d6 due to it being a slayer weapon along with the strength modifier damage of +7 which gives an average of 116 damage.