How are Pokemon games ordered in terms of plot/lore?

The Pokemon games in order of plot based on Bulbapedia:

1. Red, Blue, Yellow, Ruby, Sapphire and Emerald. All their remakes occur at the same time. Let's Go Pikachu/Eevee is thought to occur at the same time in an alternate universe, since it features the same story as Yellow in beating Team Rocket but has changes to Red, Blue, and Mina that aren't consistent with the main story (source 1 and 2).
2. Gold, Silver, Crystal, Heart Gold, Soul Silver, Diamond, Pearl and Platinum
3. Pokemon Black and White
4. Pokemon Black 2, White 2, X, and Y
5. Pokemon Sun and Moon. Pokemon Ultra Sun and Ultra Moon occur at the same time but in an alternate universe.

It is not yet clear where Pokemon Sword and Shield place in the timeline.

The order of the plot means little for the actual stories for each game though. Hence I would not recommend playing them in order of the plot, but rather play them in the chronological order of game release e.g. Red & Blue to Sword & Shield, starting with Fire Red in your case. Or alternatively start with Sword & Shield, as it's the most recently released game and hence more people are likely to be playing that currently than the other games - that helps for finding people for trades, raids etc.

Pokemon games are separated by generations, you could also easily just start chronologically and be fine as well but with your current list of games you should play:

Either Pokemon Leaf Green or Let's go which are both just remakes of the Gen 1 games of Red and Blue. If you prefer the 2d games which are more classic go withe Leaf Green but if you want a more streamlined and modern experience go with Let's go. The rest is really up to you from there.