Well, heavy weapons is a pretty easy one because the meta right now is rocket launchers.
If you are running with machine guns, you are either playing in a group or playing against a lot of bad kids.
There are some great exotic heavy weapons for crucible, but as previously stated, that takes away from having the best exotic primaries.
The Truth is probably the best heavy weapon in the game. It has aggressive tracking as well as proximity. It also has three in the chamber, which is very nice to have.
Gjallarhorn is very good as well. It has weak tracking, but it has a hidden perk of grenades and horseshoes, so it will also detonate on proximity. It also has wolfpack rounds, which get kills in PvP that they have no business getting.
Thunderlord is a great machine gun, and both looks and sounds cool. It is still a machine gun though.
As far as Legendary rockets go, there are several really good ones. You can get Tommorow's Answer in trials, which already has a very good pvp roll on it. Other good choices are an Ash Factory, which drops in crucible or maybe a Radegast's Fury, which drops in Iron Banner.
You mostly want the same thing on all of them. Warhead Vaneers in the first slot. Either clown cartridge or tripod. In the middle section you will want Javelin. In the final slot you of course want Grenades and Horseshoes.
Proximity is so powerful right now that not using it is gimping your game during heavy round.