Secondary weapons are very important most of the time and can vary depending on your playstyle. Some people like to run a Last Word and Sniper Combo. Others may run a Thorn and Shotty combo. Hipsters may run Mida Multi Tool with a Sniper for the ultimate in camp.
There are two things that you will notice about secondaries. The best ones are not exotic, and ammo is a lot more scarce.
First of all, lets talk about fusion rifles. Almost nobody uses them, and for good reason mostly. They have been nerfed pretty hard from what they once were, and I tend to think that they get starved for ammo since the special ammo nerf. They used to be amazing in crucible, now they are usually outclassed by either a shotgun or a primary weapon. I only know one player who ever uses them outside of bounties, and even he switches to a shotgun when in the midst of some sweaties.
Exotic fusion rifles include Plan C and Pocket Infinity which both used to be absolute beasts back in the day. Now they are merely "good", and Pocket Infinity is hard to use with a lack of special ammo available.
Second, perhaps the most hated gun in crucible, the shotgun. The only real choices for shotguns in my opinion are the high impact ones. Felwinter's Lie, Party Crasher +1, The Judgement, and Matador 64 are all in the top tier of shotgun. Proper rolls for best effect should be aggressive ballistics in the first tree, whatever you want for a second perk (although I recommend knee pads, luck in the chamber, or final round), something to increase range in the middle tree, and the most powerful shotgun perk in the game for your final perk....shot package. Shot package is so important because it reduces the spread of your shotgun over distance giving you a much further one hit kill range. If you have ever thought to your self......"What the fuck? How did he kill me from there?", you will most likely find that it was a shot package shotty.
If you really want to try out the exotic shotguns, feel free. They usually lost to all shot package shotguns, but can be good in different situations. The Universal Remote is useful if you really want a shotgun for close range and want to use your favorite legendary sniper as well. You can also run a full troll build with double shotgun. The big advantage to the UR besides looking really cool is that you pretty much always have ammo for it.
The Invective is also outclassed by shot package shotguns, but it is amazing for one thing. Taking out blade dancers and sunsingers. The full auto fires very fast, and can take out either of those supers without so much as blinking an eye.
I am no expert on Snipers, but know what is good generally and what is not. Depending on game type, you may want a couple of different snipers. For Skirmish and other revive game modes, you will want to use something with high impact that can still headshot kill revived enemies. Her Benevolence is the best of these currently available, and probably the best PvP sniper overall right now. Another very good sniper for 6 man modes is the Low-Grade Humility. It has very good aim assist and a decent rate of fire.
On most PvP snipers, I see people running with Hidden Hand, which increases the stickiness of your sights when moving it across your enemy. Most like the have snapshot in the middle column for that fast ADS, and unflinching in the final column to help reduce flinch a bit when being shot. Finally, there is the scope. Most PvPers seem to agree that shortgaze is probably the best sight as it has good added aim assist and is not too big of a zoom. Other favorites inclide Ambush (which has no aim assist and a wider view), and Longview SLR10. Try them out to find what you like best.
Again, I never use exotic snipers in PvP. Patience in Time is actually quite strong as it has a very high aim assist and very low kick. Ice Breaker respawns ammo and has a pretty good scope and high impact. It doest however kick like a mule, and I feel like there are better options for snipers that will allow you to use an exotic primary.
Next up will be optimum heavy loadouts.