I thought it was amazingly done. I think it showed that Amazon learned it's lesson from the bastardization of LOTR. They stayed true to the content, while formulating a compelling, original story. There was SO much fan service in that first episode. It's like they took the scenery from different parts of all the games and just plopped it all into a TV show. The radios, the cameras, the advertisements, the consumables, the nature of stimpaks...it was all like the game. But it wasn't in your face. If you've never played the game, you won't get lost.

I like how they kind of took FO3 and FO4 and combined their intros into a plot, then went on their own route with it. They even left the spectre of the enclave/institute right there for everyone to see, but it was subtle and just well written and acted. Even when they took a bit of current cultural disagreement and threw in the "Non-binary" character, it wasn't rammed down your throat in an unspoken lecture. It was just another character.

Main Characters -

Lucy - "The loan wanderer". Perfectly written as a naïve vault dweller participant in a sinister undercurrent plot about the evils of humanity
Maximus - Knight aspirant - Part of the more dogmatic western faction of the BoS. So well written and performed. It showed the flawed nature of an otherwise noble venture.
Cooper Howard - "The Ghoul" - A lightly referenced, consistent character from game lore that was kind of like the Roy Rogers of the series. I love that they kind of turned him into the Vault-tec rep from FO4. It's great.

The only real criticism I have for the show is that it moved a little slow in ep.1. I'm sure it will speed up, though, so not a big deal.