Are these games in any way connected to each other? Story wise. I dont have time to play any previous game, if its really good as people say I will jump to F4 directly.
IMO, Fallout 1, 2, and NV are pretty connected (heck in Fallout 2, your character is the grandchild of your character in Fallout 1).
There are a number of people in Obsidian who were on the Black Isle team that created Fallout 1 + 2 so they included many references in New Vegas. Basically, there was going to be a Fallout 3 codenamed Van Buren, but Interplay went bankrupt and sold the rights to Bethesda who made the Fallout 3 we know. When Obsidian was asked to make NV, they took ideas from Van Buren.
I honestly had a hard time seeing how Fallout 3 had any relation to the series... Sure, they threw out names like Brotherhood of Steel, Enclave, and Super Mutants, but it just didn't feel like part of the universe.
Fallout 1 and Fallout 2 (especially 1) are pretty dated though so it might be hard for newcomers to get into (doesn't stop me from playing them yearly).
Fallout 1 needs
Fallout Fixt to help it run better on modern computers and remove most bugs. The best part is it's still being updated. I believe the next update is when the creator will move Fallout 1 onto the Fallout 2 game engine which should help immenesly.
Fallout 2 needs either the Unofficial Patch (recommend for first time) or the Restoration Project (a lot of cut content, but really fun). You can grab them from the bottom of the first post
here.
Just remember that Fallout 1 and 2 are really old school - they don't have things like quest markers and such. You really need to talk to people, explore, and save everywhere. Fallout 1 does have an annoying time limit though (I think depending on which Fallout Fixt option you choose - you can remove it).