In terms of how straining each role is and how much they affect the other players in their team...
I think for the classes, the most important role for the Team is the Trapper, because the Trapper of course controls capturing and encasing the monster in an arena, which sets the stage to really combat it, and often is the one tracking it as well. Locating the monster is often on its shoulders (other characters in other classes can help though, such as Bucket or Val can tranq it if she sees it), and using the barrier at the correct time is so important. With a bad trapper, the game can be just a series game of hide and seek where the Hunters can't really do much until stage 3. With a good trapper, the whole entire round and dynamic of the game can change so greatly.
Medic probably comes second as they have to concern themselves with the well-being of the team, less setting the pace and more monitoring how everyone is doing and who needs aid, and making weakpoints for the other users, or speeding up the team/tranquilizing the monster, depending on which Medic you play as. Each Medic character has a unique helpful trait outside of healing (Val being able to tranq the monster, Lazarus being able to make so many weakpoints on the monster quickly so others can do buffed damage, Caira being the ability to speed up the team temporarily to follow the monster much faster (and a stronger offense than the other Medics)), which makes them also invaluable outside of healing/reviving.
Support comes next, as shielding other users at crucial moments can be a lifesaver and turning people invisible when needed can aid the team so much, plus the Assault is the most likely class to clutch and survive when the others are dead while waiting for the drop-off ship to arrive. Shielding and invisibility can save lives and matches, if used correctly. Plus random things that can help, like Bucket's ability to track the monster from an aerial view, or Cabot's ability to quickly reveal all life in the nearby vicinity.
Assault is probably the least straining position, but not to say least important at all, as its the one that can most bring the damage to the monster and really chip away at its health, but by its role as a heavy damage-bringer, it doesn't need to concern itself with the well-being of the others as much and just focus on killing.