All three are excellent choices for different reasons and you'll probably enjoy every single one of them considering the games you mentioned you like. Skyrim is probably the safest choice since you mentioned how much you like Bethesda's Fallout games, and Skyrim is more of the same, albeit in the Elder Scrolls universe. It's greatest strength is in its world design that offers an amazing amount of exploration and environmental storytelling that you will probably be into if you like Fallout 3 and Fallout 4.
New Vegas plays like a Bethesda game, notably Fallout 3 since its all in the same engine and plays exactly the same. But it's the quality of the content itself that is the most significant difference, in that New Vegas offers so much more in terms of writing, quest design, characters, factions, and role playing. So many choices in how you want to go about a number of different situations in the game world and to further define your character. I would agree with the sentiment that New Vegas is up there in being the ultimate RPG experience.
The Witcher 3 excels the most at its characters and story, while also shining in some areas similar to New Vegas with some great quests and writing that almost always offer a choice to be made, sometimes pretty difficult choices. You can't role play like in Fallout since you're a set character, Geralt of Rivia, but there are ways for which you can decide how Geralt can act through dialogue. Again, not as nuisance as New Vegas, but it's there. Not to mention, this game has some of the greatest DLC you will ever play that offer amazing stories to experience.
Again, all solid choices and you can't go wrong with any of them. For your sake, I'd say play Skyrim then New Vegas and then The Witcher 3 in an order of games that starts from what you're most familiar and then getting to games that further differentiate from that.
Me personally? I struggle to decide whether I like New Vegas or The Witcher 3 more. Both are such equally good RPGs. I'd definitely say they surpass Skyrim, but Skyrim has its own strengths that can put it above both of them in a few areas. Like mountains. Such neat mountains.