Grizzly is worth keeping. I've been trawling for rare pistols to get cores and actually had her drop twice, so now she's 2x for free \o/
Current 5*s are FAL, Grizzly x2, NTW-20 and Vector. Jury's out on FAL and NTW because I only got them recently and have no cores ever.
After that at 4* it's M1918, the Plot Squad (M4A1 etc) SVD, Springfield and MP5.
So far I've been finding one of the most important characters are the MGs, because they can seriously whittle down the horde before they even get a chance to attack you (reducing the amount of fire you'll take). My highlevel murdersquad sits at >6k CE with two 50+ MGs, my two best SMGs and a pistol in the middle. It's pretty much built around the MGs murdering everything every n seconds. ARs are good at finishing off stragglers and I haven't yet wholly figured out how to leverage my army of bajillion rifles effectively yet.
I'd been worried about the gameplay boiling down to nothing but 'do I turn auto-skill on immediately or not' but it's getting a lot more interesting now I'm in Chapter 4 and you get things like the artillery bot that forces you to shift your formation around. Add in a few skills that really need to be manually activated, and the fun-if-dangerous game of 'when do I withdraw my SMGs to kite?' and its getting a lot more interesting.
oh and I still don't have any AP ammo.
EDIT: GRIZZLY JUST DROPPED FOR THE THIRD TIME AND I STILL HAVE NO AP WHAT IS MY LUCK DOING