UPDATE 2025
Now that Arcane slots are available we can use either

• Secondary Outburst: this provides the maximum possible DPS but requires you to run either crescendo Furax Wraith and get finishers or Ceramic Dagger melee and get primary kills first
• Secondary Fortifier: this is the most "chill" option since it can generate overguard as you hit eximus enemies which helps with survivability, and also deletes overguard from eximus/thrax much quicker
• Cascadia Flare: provides decent amount of base damage but again this is additive to both galv shot and [Mesa]'s strength multiplier

This is best used in combination with Nourish on Mesa, since Nourish provides Viral damage, and is good for both Grineer and Corrupted enemies.

MOD BREAKDOWN

• Galvanized Diffusion - mandatory multishot multiplies damage by up to 3.3x
• Galvanized Shot - this gives +120% damage per status which is additive to the damage bonus provided by ability strength. Having a maximum of 5 statuses (IPS + heat + viral) after a few seconds of shooting gives +600% dmg, which is approximately a 69% DPS boost. Having just 3 status will allow Galv Shot to be better than Anemic Agility or another element mod.
• Primed Pistol Gambit - mandatory CC
• Primed Target Cracker - Mandatory CD
• Lethal Torrent - gives more ire rate and multishot.
• Primed Convulsion + Pathogen Rounds - gives raw corrosive damage which has +50% bonus against Grineer and also partially strips armor up to 80% at 10 stacks.
• Primed Heated Charge - gives raw Heat damage which contributes to total damage, and heat procs can also strip a further 50% armor which is multiplicative with corrosive (giving 90% maximum possible partial strip).

Flexible Options:

• Lethal Torrent vs Primed Expel :
  Lethal Torrent is 21% better than Primed Expel if you DON'T OWN ARCANE VELOCITY but only 3-5% worse about than Primed Expel WITH Arcane Velocity. Note Lethal Torrent is effective against acolytes and thrax while Expel mods do not affect them. If you want to min-max Regulator damage against a specific faction eg in disruption, then you can use Primed Expel over Lethal Torrent.
  Lethal Torrent is always better than NON-PRIMED EXPEL.
  Lethal Torrent is better than Galvanized Shot above 335% ability strength when accounting for 5 status effects.

• [Anemic Agility] if you don't own [Lethal Torrent] or Galv Shot.
  Galv Shot is 21% better than [Anemic Agility]
  Lethal Torrent is 7% better than Anemic Agility WITH Velocity but only <1% worse than Anemic Agility WITHOUT velocity.

• [Creeping Bullseye] if you don't own Primed Pistol Gambit.
  Primed Pistol Gambit is 4% better than Creeping Bullseye (with velocity) and 10% better without velocity.

• [Hornet Strike] is a last resort if you don't own [Anemic Agility] or [Galvanized Shot].
  [Hornet Strike] is the worst option, being 8% worse than [Anemic Agility], 16% worse than [Lethal Torrent].

Variants:

For Corpus : Switch [Primed Convulsion] for [Pistol Pestilence] and [Primed Heated Charge] to [Anemic Agility] for pure Toxin (Bypasses shields)
For Murmur: Swap [Pathogen Rounds] for [Accelerated Isotope] to make pure Radiation
For Thrax: swap [Lethal Torrent] for Magnetic Might