Both are correct, while the first is more common in modern spoken English. The second one you would find in writing, rarely does anyone speak like that.

There’s a difference in emphasis. Also possible are I would’ve never said that. (In writing) I’d’ve never said that. (In speech. Probably the most common thing to say. No need to waste syllables)

Both are correct. To decide between the two, think about which word you want the adverb "never" to modify. Which is more important to you? Which one do you want to emphasize? (1) "never would" puts the emphasis on "would" (I WOULDN'T do that) (2) "never said" puts the emphasis on "said" (I wouldn't SAY that)

Both are correct, but I think the first is common

"I would've never said that!" is perfect!