He's going to become a paladin because this is Blizzard we're talking about.
They're hammered it into our heads repeatedly that Anduin just isn't good at physical combat, so naturally being Blizzard they're just going to handwave that and ignore it. They've also been on some kick lately between the shit like Delas Moonfang and paladins coming to the rescue of priests that paladins are just superior to priests and there's no reason for any Light-wielder not to be a paladin.
By all logical reasoning he shouldn't become a paladin and the only evidence supporting him becoming one is picking up his father's sword, but again this is Blizzard. A company whose writers mainly grew up on comic books and other garbage notorious for ignoring logic and going with whatever looks cool. So yea, he'll be a paladin.