As far as I can tell, you can play each of the Fallouts separately without missing much. Sure there will be references that will have deeper meaning if you played the earlier game(s), but nothing to stop you from enjoying the individual games on their own. F3 takes place on the east coat while F1 and F2 take place on the west coast, very near yours truly as a matter of fact.
You can get the gist of the backstory from wikipedia and also, for those who don't have F1 or F2, you can play them for free by signing up with Gametap.
Since you're an old fogie like me, I have confidence you'll enjoy the charm of the old isometric POV and dialogs, so feel free to play in any order you like.