Huge fan of the Fallout series, and one of the things I loved the most is that none of the games require the others. The storylines for Fallout 1-4 and Tactics all happen at roughly the same time (over a period of 116 years) but occur on top of each other in different places. Each of the stories is crafted around a unique character that is "introduced to the world of Fallout" for the first time. Knowing the stories from the previous games only results in a few meaningful (and usually humorous) moments. For example, the first third of Fallout 1 is trying to secure a new water purification controller chip for Vault 13. You'll likely be level 10-15 or so when you finally find it, after scouring the Wasteland and having your life thrown into chaos, leading to the later portions of the game. In Fallout 2, two generations later, your player character goes to a place called Vault City (originally Vault 8) looking for a G.E.C.K. and may stumble upon this as part of a larger conversation:

Player: "Did your vault receive any extra equipment?"

NPC: "Some. A whole shipment of replacement water chips. About a hundred or so. Not sure why, as we've never had any trouble with our water system..."

Not verbatim, but you get the idea. It's little quips like this that can be LOL worthy, but nothing important.