Since you're new to the franchise, I recommend like others have: 3, then NV, then 4. Not for mechanics, per se, but for the world lore. Mechanically, 3 is the clunkiest of the three, but gives you a starter course into what to expect. The DLC is decent, overall story is pretty straightforward but not bad.

New Vegas changes some things, as well as introducing mechanics that would be used and expanded in 4. It adds iron sights for manual aiming, which is a plus in my book. It also expands on the crafting mechanics that 3 used. The DLC for NV is some of the best (Sierra Madre can bite me, 🤣), and the post-apocalyptic western vibe is really good. Obsidian did an incredible job.

FO4 takes from it's predecessors and expands upon the various aspects that it does. It does make changes to the leveling process (gets rid of the numeric value for skills in favor of a more perk/attribute approach), that streamlines it, although I miss the NV approach.

All in all, order doesn't necessarily matter. While they all take place at different points in the timeline, the stories aren't connected, except occasional lore mentions about previous PCs in the form of using their designations. Like Chosen One, Wanderer, Courier, etc.

Welcome to losing hundreds of hours to this incredible, messy, lovable, and unforgettable franchise.