Forgive me if you already know this, as I'm assuming you don't, but every series they had has been rebooted since then. If you haven't already done so, look for the first issues from the the new series and see if you like the directions they went into.
If you're interested in the story started at the beginning of Rebirth, I suggest Detective and Action Comics. They've had a few tie-ins to the overall story. If you like Batman and the Flash, look for issues 21 and 22 of both the new series. The made up a crossover about the main Rebirth Story that was cool. Also, they started a new Justice League series you may enjoy. I also recommend Justice League vs. Suicide Squad if you want a serious action story.
The current "Metal" and "Doomsday Clock" events might be places to jump on regarding the state of DC in general.
Like he said, Doomsday Clock covers the present state of the DC Universe. Also, (personal opinion), you seriously need to check out Dark Nights: Metal. It involves tie-ins from a few of their comics, and it can get dark in some parts, so it isn't for everyone. But if you like Batman, you might enjoy the story they've been telling there.
I don't know all of your preferences, but these ought to help you understand what's DC has been up to.
I say Artemis. The two can probably match each other in terms of strength and fighting skill. Artemis' main setup includes a variety of weapons topped off by magic axe that works like Mjolnir, so she packs a better arsenal. Garth's power set gives him an edge, but because he took a vow to not use magic, he's almost never at full power. At full power, he could probably win, but since's always holding back, it comes down to strength, durability, and fighting experience. Artemis, trained from the age she could form a fist(mild exaggeration) has the edge. So i say she wins.
I'm thinking Cassandra. Connors best feat in post crisis was holding his own with lady shiva. I think post crisis Cass has the feats to suggest that at the least a fight between her and post crisis shiva wouldn't be a stomp.
This is N52 Cassie, and I honestly doubt she has the feats to stand against Hawke.
In Detective Comics #955, N52 Cassandra squared off against around two hundred members of the League of Shadows alone. These are ninjas more dangerous than Ra's al Ghul's League of Assassins. She was able defeat every one of them without killing them, and still had enough left in the tank to throw down with her mom, who was arguably a better fighter than anyone in the Bat Family. She couldn't beat her alone, but that's a testament to her skills.