first off; first thing; first of all
Emphasizes doing something before anything else; similar to いの一番. Often used in casual speech or instructions.
See also: いの一番
Finish your homework first thing.
At first, he didn't believe the story.
いの一番 is a more idiomatic and emphatic expression meaning 'the very first thing', often used in set phrases like いの一番にやる. 一等最初 is slightly more literal and less idiomatic.
最初 simply means 'first' or 'beginning'. 一等最初 adds emphasis, meaning 'the very first' or 'before anything else'.
Compound of 一等 (first class, number one) and 最初 (first, beginning). The exact historical derivation is uncertain, but it likely arose as an emphatic adverbial phrase.