I tried to organize them all properly, but going through all 43 mods made me see its not as clean as I would like it. Not wanting repeats, I just decide to throw in whatever fits together and hope its clear enough for you to follow. Note that the Prism and Seismograph perk changes how some of the mods work if you choose to use them. All weapons mods are white for consistency.

This guide is made for the purpose of keeping track of the weapon mods that exist in this game and to plan future builds for future runs/turret trial attempts.

One more speed mod can be found in the knockback section.

Turret Mod Database: Link
Mutation Database: Link

I'm not exactly satisfied with the list, but this is how I think this is how to best do it with the weapon mods available. If you got a better idea on how to improve this, let me know for consideration. On the chance I happen to miss a weapon mod, please share me a screenshot of it and I'll amend it when I have the chance to.

UPDATE 1: Added a couple of screenshots (Size/Firerate, Damage/Firerate) I forgot to add thanks to Lazice comment.

Screenshots taken and cropped by me.