Fallout 2 is it's superior in every way.
Funny that this was actually a debate back in the day when Fallout 2 was the "new sequel." The applauds for Fallout 2 were many. It is an interesting game and the world is much more expansion, there are so many more stories and interactions, and so much more to play with.
That said, Fallout 2's strengths were also a weakness. The Enclave was simply not that interesting a group of bad guys as the Master and his army and while the story had "more stuff" it kind of lacked the narrative focus, the need for resolution, that Fallout 1 has. Don't get me wrong, Fallout 2 is a very good, if somewhat flawed, derivative of Fallout 1, and a fun game.
But I would argue that Fallout 2 is where we begin to see the breakdown begin, where we lose sight of the world and it starts to fall apart. The Law of Entropy begins in Fallout 2. While New Vegas was, in some ways, a return to the Fallout 1 and 2, in terms of his focus on story and atmosphere, and so an effort to get back to the core, in the end, New Vegas also has its problems. New Vegas reminds us that the form of Fallout 3 could be married with the story of Fallout 1 and 2. But even New Vegas has way too many flaws and was also an incomplete project, with the modding community filling up the big blanks and problems.
But Fallout 1- gives us the first vaults, the problem of the waterchip, deathclaws, the first gangs including the Khans. Think of the places- Shady Sands, Junktown, the Hub, The Boneyard. Or the factions- The Followers of the Apocalypse, The Brotherhood, supermutants? There is so much plot here- FEV, the original cause for the ghouls, Necropolis, the Water Merchants. Remember the first interactions Harold before he becomes a tree. Or Dogmeat? How many players got chopped to pieces because Ian got happy with a submachine gun? How many of us remember struggling how to save Dogmat from being fried? Back then the weapons were very generic because the writers didn't have the pressure to appeal to public pressure. They could make a creative game out of their imaginations. Fallout 1 is a great accomplishment. The others are all derivatives.
Fallout 1 is the creative bedrock of all the other games to come after it. The original Wasteland might have been the initial spark, but it was Fallout 1 that created the world that all other Fallouts owe their origins. You can't really understand the Fallout world, without Fallout 1.
My list would have started with Fallout New Vegas, and then Fallout 1 and 2. I am not sure if I would do Tactics before Fallout 3. But what about the original Wasteland - the game that gave us "The Junkmaster" and the original Rangers?
https://en.wikipedia.org/wiki/Wasteland_(video_game) . A classic game and, just reviewing the plot, you can see how Fallout 1 was its descendant. I am sorry CT, but Fallout 2 is a wonderful game, but it suffers from its own core ambitions.