[cf. Gabler 3:1]
What if Joyce started off with "Buck Mulligan was stately and plump. He came from the stairhead, bearing..."? It sounds a little simpler that way, more American, a little more Dashiell Hammett or Hemingway. But he didn't.
We'll see that Joyce almost always values sound and associative nuance over simplicity. [And by "associative nuance" I mean that jamming the adjectives "stately" & "plump" directly up against their referent, Buck, he's invoking the old Homeric epithet style, like "gray-eyed Athena" or "resourceful Odysseus."]
Another effect of this not-so-strange-but-still-distinctive beginning is that, compared to the Americanish alternative, the narrator is in a less visible position. To say "Buck Mulligan was..." is to put a narrating storyteller clearly on the stage; it draws a frame around the events. Putting "stately" first puts us more inside the frame.
And about "stately." It's not a strange word, not an unapproachable word, not an unfamiliar word... but it calls just enough attention to itself to stand off the page a little bit. Joyce's narration always seems normal at first glance in these early chapters, but the more weight you put on it, the more you see how it presages the big weirdness that comes later. The question of "who's talking" is never as cut & dry as it seems.
So Mulligan is stately and plump. We'll meet Stephen in a minute, who is skinny and nervous. If we were casting Mulligan, we'd need someone a little officious, with a touch of wickedness and a sharp wit, a little aristocratic, a little paunchy, someone not entirely in control of their appetites but who's comfortable with that.... a young John Malkovitch, perhaps?