Further thoughts:
Tachibana is a tiny little thing, but it's amazing how threatening someone can be when you give them the _Terminator_ treatment of being slow but unhinderable.
An excellent choice, especially given that she gets rehabilitated (in the audience's eyes) later.
What's my recommendation?
It's worth a watch. _Angel Beats!_ uses heavyweight parts without becoming overbearing. It's not particularly challenging despite looking risky.
I wouldn't watch it if you're in the middle of a deep depression, but it's a good pick, I think.
Is that okay?
It's probably better than having an actual showdown with God. _The Devil Lady_ could pull that off, but it's super risky. It's very easy to have a broken moral or metaphysical story, and I think _Angel Beats_ is better for choosing not to go there.
And that fight is, ultimately, unresolvable. Yuri can forgive herself for not doing the impossible, but she can't forgive God for making the world cruel. And she doesn't have to. The metaphysics here are such that it's her own heavy heart that keeps her here.
This is even made explicit in the show between Otonashi and Tachibana. No one has much reason to fight among themselves.
The doppelganger and shadow crises are actually opposition, but the real fight is between Yuri and God.
Now, this isn't a comedy, but in a way it's a comedy of errors, in that most of the conflict is driven by the misunderstanding that people are on different sides when they're really not.
The Yuri/Angel conflict is mostly confusion as to what their goals actually are.
I'm not a fan of the implication in Another Epilogue that Otonashi stayed on, like the Programmer before him.
Given that, and the goofier tone of the OVAs, I recommend just the core series.
It does a solid job of setting up the tension, bringing it to a head, then resolving it. At the climax, you feel pretty solid.
The original ending is a little ambiguous, but not in a bad way.
That's the show.
So, what's my takeaway?
First, despite what some people have said, this is not a comedy.
There are moments of humor, but it's basically earnest the whole way through. (The OVAs are more comedic though.)
A new student has figured out that this afterlife is bullshit. If he gets good grades, will he go to heaven? It's a farce!
His rant is cut short when he's confronted by the Student Council President...
Otonashi.
If you see it, then quit whining and seize the day, he says.
Yuri declares an operation: everyone should pretend to be in high spirits all day. When they don't vanish, this should confuse Angel so much that she calls God over the irregularity.
This fails to work.
For Golden Week, Yuri sets the team to a battle royalle.
The goal is for the most final survivor, the most vicious, to be so dangerous that Angel falls back to call God for help.
Instead, shenanigans ensue.
But are there OVAs, you ask?
Yes. Three of them.
Two bonus episodes that sit between episode 2 and 3 and between episode 4 and 5, and a tiny thing (2 minutes) called _Another Epilogue_.
They both pass on, but a post-credits scene gives a strong implication that they will meet in the next life.
The last ones out are Otonashi and Tachibana. Otonashi suggests maybe they should stay to help the next class, and even confesses his love.
Tachibana explains that what was keeping here here was him. She had a heart transplant, and he was the donor.
Yuri awakens three days later. Almost everyone has passed on. The only ones remaining are her, Otonashi, Tachibana, Naoi, and Hinata.
For the sake of form, and for closure, they hold a graduation ceremony, and a few last words before they pass on.
She doesn't want to.
She destroys all the computers, hopefully resetting the NPCs.
As she breaks down, weeping, she sees a vision of her younger siblings telling her she doesn't have to carry the weight all by herself.
Falling in love should be an auto-exit, but he was trapped here. He created the shadows so he could become and NPC.
It is Yuri's love for her friends that has triggered the failsafe. But she is here in the core now, and can take control and become God if she wants to.