For PvE all around, HoPF Sunsinger and Obsidian Mind Voidwalker, especially with Bad Juju in the mix.
These are both good in PvP as well, but you can get some fun specialty builds using Claws of Ahamkara and Monte Carlo. Skull of dire Ahamkara can be interesting too without being necessarily OP.
I realize I didn't actually answer myself...
PvE (Sunsinger)- HopF
PvE (Voidwalker) - Obby Mind (Bad Juju is the obvious pairing indeed)
PvP (Sunsinger/Voidwalker) - Voidfang Vestments
Shoutout to Starfire Protocol as an all-around useful Sunsinger set. It sucks that you can't equip three grenades, but Touch of Flame can steal tons of kills for you, and IMO Angel of Light is a deeply underrated ability.
Claws of Ahamkara is a total blast. Multiple things you can do with it. You can even jury-rig a poor man's Nova Bomb factory with Bad Juju and Soul Rip if you don't have Obsidian mind or need to use your helm for something else.
Light Beyond Nemesis (as the twin Crests of Alpha Lupi before it) is just a lovely PvE exotic piece, a wonderful choice anywhere in the game except Hard Mode raiding (and even there, the extra orb creation is underrated).
Apotheosis Veil is the ultimate choice for HM Crota, and can lend itself to fun theorycrafting for Radiant Skin/Radiant Will builds in the Crucible (since Fireborn nulls the Exotic effect, you'll have good reason to switch your super usage up entirely).
Sunbreakers got a terrible rep for being so common early on. The Carpet Bombing solar grenade high int build from the old days is just as effective in Control now as it always has been. Not very useful in PvE though.
Sooo how do you best use the Skull?
besides most specials sucking in PVP
Could you... please clarify?
All I do is run TLW, and sometimes Thorn, Red Death, or Mida if I'm bored but that doesn't mean I don't like to see variety in the crucible.
"<insert shotgun name>" would appear to me to be plainly more common than any of the above weapons, so.... uh.
I think it'll also hurt the specials in general since when you do have ammo, you want something which is most applicable to the majority of situations which tends to be a shotgun with how small the maps are.
*shrug* Fusion rifles are actually applicable in more situations by far. Regardless you should have to think about
when to best use your special weapon, rather than applying your special weapon to every problem without consequence, especially considering how effective and not at all suck they tend to be...