The optimal build for the great majority of Crit-viable Rifles.

Primed Cold (Cryo Rounds) is pretty much always better than 60/60Cold, even when you count the damage increase from the +SC through Viral, so you'll want Primed Cold on pretty much all your Rifle builds.

A Faction(Bane) mod can be used instead of another mod for long runs involving external stat buffs. I.e: if you play with a [Wisp] who offers +FR buffs you should replace the FR mod ([Vile Acceleration]). But for runs not involving external buffs you don't gain much extra damage from a Faction mod, because Rifles have stiff competition for mod slots now, making that downside of only working on one faction a lot more relevant.

Riven

Riven stat priority: CC = CD > Dmg > Toxin > FR > MS
CC > CD if below ~90% final CC cuz increased HunterMunitions reliability, else CD > CC.
Riven replaces mod with same stats, in reverse priority; i.e: replace the mod with the lowest priority stat your Riven has. But don't replace [Galvanized Chamber] even if Riven has MS. MS is such low priority because GalvChamber brings a buttload of it.

Arcanes

Merciless is the easy all-round option that is especially effective on low-ammo and weapons with low shooting:reload ratios.
Deadhead is the more niche option for precision weapons where recoil might be an issue, or where the headshot multiplier bonus can be abused.
Dexterity is mainly useful as a stat-stick for your melee by increasing Combo Duration without taking up a mod slot in your Melee weapon.

Good Exilus mods

Vigilante Supplies - The only option that provides a tiny increase to your damage, while also bringing you extra ammo.
Stabilizer - Nice for reducing Recoil on weapons where that is an issue.
Twitch / Tactical Reload - Nice utility.
Sinister Reach - Can only be used with Beam weapons, but is generally the obvious choice there.
Terminal Velocity - Good for weapons with damage-falloff, but useless on all others.