So it is direct color matching? I expected something more in the line of rock-paper-scissors.
I still have a long way ahead leveling the sunsinger. Right now it is not reliable, so I equip it before claiming the bounties.
Yup, direct match. Solar damage for Solar shields and so on.
As you progress in the game, it'll really help out to have a good shotgun and a good sniper for each element. Later, playing Raids and PoE and ToO you can also get primaries of each element.
From Vault of Glass, you can get:
Arc Hand Cannon (best PvE primary) * exclusive to Heroic Vault of Glass
Arc Pulse Rifle (it sucks) * also Heroic-only drop
Solar Scout Rifle (super good)
Void Auto Rifle (super bad)
Exotic Solar Primary Fusion Rifle (good) * Heroic
From Crota's End: * all primaries exclusive to Heroic
Void Hand Cannon (ignore the hate, it's solid)
Arc Pulse Rifle (it's OK)
Arc Scout Rifle (it's good)
Solar Auto Rifle (it's an auto rifle so it sucks)
Exotic Arc Auto Rifle (lol so bad it hurts)
Trials of Osiris has a full suite of primary weapons. If you go flawless, you'll get a random Primary as a reward, with a random element. So you could get a Solar Hand Cannon or a Void Pulse Rifle or whatever. Except for the Auto Rifle, which sucks because it's an auto rifle, they're all extremely good weapons.
Likewise Prison of Elders at level 35 can drop a primary from Skolas with a random element. Unlike Trials, it's not guaranteed. They're actually very rare drops but they're universally underwhelming so nobody cares anyways.
Sweep up the good stuff from VoG/CE and you'll be set for Nightfalls with any burn