Is there an explicit reason for -o, -a, -e, -i? The longer ones vaguely remind me of similar words/constructs in different languages that influenced Esperanto, but the very basic ones seem completely random. Is there an origin story for this choice?
Interestingly, Wiktionary has an etymology for all of these:
From the masculine singular of the Romance languages, such as Italian (amico); perhaps also the neuter singular of Russian (окно (okno))
From feminine singular adjectives (and nouns) of the Romance languages, such as French ma, Italian mia, Spanish mía, fría.
Perhaps from Latin deponent verbs such as loquī (“to speak”).
From the Latin and Italian adverbial suffix -e (as in bene "well"), perhaps reinforced by the Russian adverbial -e found after a palatalized consonant.
However, none of them have a citation and they don’t really seem particularly convincing. For example, in Spanish the -o ending is also used for masculine adjectives and the -a for feminine nouns so the hypothesis doesn’t really make a lot of sense.
My hunch is instead that Zamenhof just wanted to use all of the vowels for the endings because they are short and can be easily pronounced after most sounds. The actual meaning which they are each assigned is probably mostly arbitrary.