I use NL Shadow a lot with high impact and full auto.

Still learning about this Aim Assistance business -- is it noticeable?

What would be some rolls to look for in PvP in your option?

I find the aim assist boosts are helpful... not drastic, but it does make a bit of a difference, and sometimes that can mean all the difference :)

If you're asking about Hand Cannon perks specifically, it's tough to say what will work out best until we get our hands on 2.0 and see exactly how drastic the range & accuracy stats have been nerfed. One thing I'm interested in experimenting with is perk combos that turn the new smaller clip size into an advantage. I'm in the process of re-rolling my Timur's Lash with the hope of getting Luck in the Chamber, Send It, and Final Round. That way 2 bullets in each clip will do bonus damage... in a clip of only 5 or 6 rounds, that's a fairly high percentage of shots with extra damage.

At the moment, I'm finding Pulse Rifles to be the best weapons overall for PvP... yes, even better than Thorn or Last Word. I was joking with TheeChaos and Ottermack last week that I'm actually happy when I see a team running nothing but Thorns, because I know I can beat them with my Pulse Rifles :) They're a bit disadvantaged at close range (especially against Last Word), but I tend to roll with a shotgun so I switch to that if I'm fighting up close.

The perks to look for with Pulse Rifles IMO are Headseeker (body shots increase crit damage for a short time) and anything that boosts stability. A sight that boosts target acquisition is always a plus, too. I've got 3 Pulse Rifles that are extremely effective in PvP:

The Messenger

Word spread about this bad boy pretty quickly. It has fantastic range and stability, and high impact. The rate of fire is slow, but the high impact and Headseeker perk mean you can kill another guardian in 2 shots. Just aim for your target's chest to land the initial body shot, and the weapon's slight recoil will naturally pull your other bullets up towards the head.

55a-allFATE

I just finished upgrading this beauty a couple days ago, and I'm loving it. It's got Headseeker, Outlaw (fast reloads), and Smallbore (bonus stability). The impact isn't quite as high as the Messenger's, but the rate of fire is higher. So the typical time-to-kill is about the same. This allFATE will almost kill in 2 bursts... if you're target has taken any damage, 2 shots is all you need. Otherwise a quick 3rd shot will finish the job.
The higher rate of fire means this weapon is a bit better at close/mid range than other Pulse Rifles.

Spare Change.25

In terms of base stats, the Spare Change is very similar to the Messenger. Slightly less stable, but more range. I rolled mine for Rodeo and Smallbore, both of which boost the stability. And of course Headseeker, which makes this gun a 2-shot kill.

Hope that helps give you a few ideas! Above all else, experiment and see what works best with your playstyle. I have a feeling that 2.0 will return Auto Rifles to much of their former glory, so it might be a good time to get some practice in with those, too.