Just want to add a list of some basic but important mods so you know what to look for. If you're in a clan you can probably just ask for any you're missing and get them for free, since a lot of people have duplicates. Asking in region chat could work, too.
Rifles:
Cryo Rounds (cold)
Stormbringer (electricity)
Hellfire (heat)
Infected Clip (toxin)
Split Chamber (multishot)
Point Strike (crit chance)
Vital Sense (crit damage)
Shotguns:
Chilling Grasp (cold)
Charged Shell (electricity)
Incendiary Coat (heat)
Contagious Spread (toxin)
Hell's Chamber (multishot)
Blunderbuss (crit chance)
Ravage (crit damage)
Secondaries:
Deep Freeze (cold)
Convulsion (electricity)
Heated Charge (heat)
Pathogen Rounds (toxin)
Barrel Diffusion (multishot)
Pistol Gambit (crit chance)
Target Cracker (crit damage)
Melee:
North Wind (cold)
Shocking Touch (electricity)
Molten Impact (heat)
Fever Strike (toxin)
Fury (attack speed)
True Steel (crit chance)
Organ Shatter (crit damage)
Warframe mods:
Vitality (+health)
Redirection (+shields)
Continuity (+power duration)
Flow (+max energy)
Intensify (+power strength)
Streamline (+power efficiency)
Stretch (+power range)
Some of the mods on this list are a bit rarer than others -- the multishot series, Vital Sense, Ravage, Continuity, Flow, Intensify and Streamline -- but it shouldn't be too hard to find people with extras.