The gunplay was clunky when it came out. FO3/NV very much had an “Oblivion with guns” feel to them.

I’ve always primarily used VATS. Unarmed or melee focused builds can also be viable, but the early game is rough.

As for mods, I would recommend a modlist. “Viva New Vegas” is one I’ve played with, currently doing a “Begin Again” playthrough - the latter adds a lot of the nicer features from Fallout 4 and includes Tale of Two Wastelands which combines FO3/NV into a single game, you can travel between each wasteland and bring all your stuff with you.

Ultimately, these games aren’t really an FPS so the shooting will always feel a bit off. The story / dialogue / environmental storytelling are really where it’s at!