Support is a weird case in splatoon.
I mean, there's no buffing or healing to speak off and you still (or better said schould) get in lots of combat situations.
To my, its a mix between defensive and offensive.
You won't be pushing nor standing in vantage spots to make the most out of your main weapon 24/7.
More like both pushing or seizing vantage spots.
A support weapon doesn't have both the pros and cons as much as defensive/offensive weapons.
Keeping this in mind, support weapons stand in the middle of things and you can take this quite literary on the battlefield.
You make sure everything that needs to be is under ink.
You make sure to ambush oppenents that sneak beyond the front line's (or ATLEAST warn your team)
You make your teammates job easier by picking enemy's from afar, use subs, ambush them while they are busy with a teammate, bring cover fire for added pressure, create weak points in an enemy team, soften them up beforehand etc.
Hel, going against an enemy team that defeated the rest of your team but is considerable weakened as a result, is a valid strategy if you now what your doing.
So although you schouldn't effectively seek combat, you schouldn't shy away from any combat also and take your chance and play 'aggresively' once the need arrives.
Like when your team pushes, bring back-up fire, pressure, seek openings to sieze major results (like sneak to a vantage point in the enemy base during a push)...
Supports schould still have a considerable kill count at the end of day too.
I play mostly support and thats how i would describe it.
A mix between defensive and offensive that sees and seizes oppertunity's by quikly switching to a defensive or offensive role.
Its a complicated manner at first but its pretty natural once you have expierence with it.
Some good support weapons are imo:
Carbon roller, bamboozler, (duallie) sqeulchers, Long barrel nozzlenose, vanila rapid blaster, both heavy splatlings.