Operation Anchorage did a decent job already from my experience. Having a whole game relating to it probably wouldn't be a massive success as it would move away from what draws people to Fallout.
Out of the games i've played i'd say:
1: New Vegas - Although it breaks a lot and has some annoying bugs the gameplay is fun and it has a good atmosphere.
2: Fallout 4 - Only just beats Fallout 3, i enjoy the settlement building and have spent countless hours creating a variety of settlements to go with each of my characters path within the game. It adds that extra layer to the role playing.
3: Fallout 3 - It has a good story and has given many hours of fun. There's a lot of variety and things to keep you busy. As above it's only below FO4 due to settlement building.
4: Fallout 76 - I've never been a big fan of the multiplayer Fallout concept and didn't get the same urge to continue playing that i did with other FO games.
As for Fallout and Fallout 2 i've got them downloaded but haven't played them yet.
I quite like ain't that a kick in the head from FNV
Cass is also my favourite :-)
My recommendations normally consist of the ink spots and such
I was waiting for that to be announced. Ultimately it's Sony's platform so not much Beth can do apart from keep helping out with mod support on other platforms