I think you should play Fallout before Fallout 2. There might be some small spoilers in F2 of how F1 ends, but ... probably not enough to worry about. Mainly it's about the world-building and settings.
The gameplay in F2 is a little better than F1 -- more freedom, I think, and less pressure to finish a major quest part within a time limit. However, F1 does an _amazing_ job introducing the setting, and making you feel like you want to play in that world (IMO). There are some things in F1 that have no analogue in F2 (that I recall), and vice-versa, which make them both awesome.
In Fallout 1, there are parts where you really care about radiation, for reasons which would be spoilers, whereas in Fallout 2 I don't recall that ever really feeling like something I was worried about. Fallout 2 has a whole quest hub (New Reno) which was very memorable, whereas I don't recall as much about F1 (granted, that was almost two decades ago. ;))
I recommend making a custom character; if you try to play a Sneaky or "Face" type character, the game seemed much harder; then again, I always ended up effectively going the sniper route, so I am admittedly a little biased.
I think the official patch for Fallout 1 actually removed the hard time limit in the original release. There's still some pressure at some parts of the game but players are no longer required to pass on exploration to rush to the end.
Some fans were unhappy with certain thematic changes in F2, e.g. the (at that time) excessive increase in pop culture references and muddying of the 50s retro sci-fi backstory.
For the uninitiated: There's a reason one of the original major Fallout communities was derided as "glittering gems of hatred" at one point. Fallout 1 had a very emotional following and what happened after Fallout 2 was a series of bad business decisions around a franchise with fans that just wanted another game in the series.
Basically Interplay tried to open the franchise to the combat strategy demographic with Fallout Tactics but had outsourced the entire game to a study with no sensibilities for the established setting or even premise of the first two games beyond "kinda like Mad Max with retro sci-fi".
Then they followed up by trying to do a console shmup with desperately oversexualised marketing (press packages contained actual condoms). Again, outsourced, and with no resemblence to the original two games at all.
In the meantime they killed off the actual in-development Fallout sequel codenamed Van Buren, which was the closest the fans ever got to a successor to Fallout 2.
Then they announced plans to create a Fallout based online game with another external company, which luckily never went anywhere (fans referred to the hypothetical Fallout Online as "FOOL" even before anyone took the idea serious).
At some point all the mismanagement and continued failures caught up with Interplay, long-time employees managed to sue for lost wages and a certain company that gave the world cookie-cutter fantasy combat RPGs with two dimensional characters bought the rights to Fallout 3, 4 and 5 (and possibly more) and created what people born in the late 1990s or later think of as Fallout today.
There were some other tearful events with ex-developers creating Fallout-like RPGs (in gameplay, not in story) at other companies (just to namedrop a few: Lionheart and Arcanum) but let's just say there were good reasons to be very angry and disappointed even before Bethesda had any chance to screw anything up.
On the bright side, Steam has Wasteland 2. I haven't played more than a week or so of it, but if you're looking for "isometric turn based combat RPG in a post-apocalyptic wasteland", it nails it. It felt like a Fallout, probably because Fallout took so much inspiration from the original Wasteland. The only thing that made it Not-Fallout was the absence of Pip-Boy or Nuka-cola.
The gameplay in F2 is a little better than F1 -- more freedom, I think, and less pressure to finish a major quest part within a time limit. However, F1 does an _amazing_ job introducing the setting, and making you feel like you want to play in that world (IMO). There are some things in F1 that have no analogue in F2 (that I recall), and vice-versa, which make them both awesome.
In Fallout 1, there are parts where you really care about radiation, for reasons which would be spoilers, whereas in Fallout 2 I don't recall that ever really feeling like something I was worried about. Fallout 2 has a whole quest hub (New Reno) which was very memorable, whereas I don't recall as much about F1 (granted, that was almost two decades ago. ;))
I recommend making a custom character; if you try to play a Sneaky or "Face" type character, the game seemed much harder; then again, I always ended up effectively going the sniper route, so I am admittedly a little biased.