Depends what you want. Fallout 1+2 are not like Fallout 3 onwards. If you want a 3D loot/shoot/explore rpg, most would probably say play New Vegas. I think I still prefer Fallout 3 mainly due to the feel of the game, but both Fallout 3 and New Vegas definitely feel a bit dated, so if that's an issue for you then go straight to Fallout 4. I've left out the elephant in the room, which is Fallout 76, mainly because, AFAIK, it's a bit different again, I haven't touched it nor do I know much about it. It's on Gamepass IIRC, so you could try it on there. Though I'd imagine most would say not to try that as your introduction to the series.
I don't recall there being any real links between the games, other than they're set in the same world, so the order doesn't really matter.
Fallout 1 and 2 have turn based combat - IIRC they're similar to the Wasteland games. I've also never touched them, so I can't comment on them. I probably should since I enjoyed Wastelands 2.
Also, I'd advise mods. Even if you don't install ones that change a massive amount of things, the mods that fix things are more than likely going to be unanimously suggested.
Fallout 3 and NV are both on sale on GOG at the moment, I seem to recall there being a reason FO3 on GOG was a better buy at one point. Maybe to do with the DRM causing issues, but I can't remember and I'd hope it's sorted on steam now. I have the steam version of both FO3 and NV and I've not had any major issue to my knowledge.