I think there are far more musicians who are not singers/lyricists than are, in which case your ‘predominantly’ is wrong!
And of course what catches different people may be quite different, as there are many different tastes in music, and what one person may fall in love with instantly another may be indifferent to, or even strongly dislike.
If anyone could answer your question for pop music, they’d be able to make their fortune writing pop hits!
For me the lyrics are usually the least important - after all, I like instrumental music as well! I think it is firstly the overall sound, of which a part is melody, and the emotional connection it may make. Lyrics can cement the emotional connection. But sometimes it is just a lyric and melody that catches me, so not always the same. Unlike what seems common on the forum, rhythm doesn’t convey any emotion or engagement to me, though in some music it may contribute to the overall soundscape.
Interestingly when I first got into music seriously lyrics were completely irrelevant (fortunate, perhaps, as sometimes the psychedelic music of the day had less than comprehensible lyrics!). By a decade or so later I started to appreciate the words, and some of my favourite music combines poignant lyrics, typically reflecting either my own life experiences, or expressing views and hopes and concerns about society and the world that echo mine, layering with the music to paint an image of life and its delights and depths of despair - one that can be different every time I hear it because it interacts with my mood, or different memories or recent experiences.