First time chicken owner! I have a Barred Rock chick that just by his behavior and the way he walks around the box, this chick has what I would best describe as chicken swagger! This chick just exudes confidence in the way it walks. He's about 3 weeks old, very slow to feather, still barely there tail feathers, and his wings are just now starting to feather out.
If you can post a pic gender might already be able to be correctly ID'd, but your phrasing makes me wonder... Is this a single chick? As in, no companions? That could explain its behavior if so.
He keeps his posture upright, is very inquisitive, always looking around, stopping, listening. I realize it could end up a bossy female, but my question is, do roosters typically display different behavior, even as chicks?
Some do, some don't, it's so unreliable I don't consider it at all, to be honest.
I also don't consider it a sign of a 'bossy' female, because regardless of the animal showing such traits, it's actually 'alert' behavior. Some males will adopt it due to early maturity and instinct, feeling like they're already looking after a flock (I've actually had males only days old already feeding their own mothers LOL, and mating and crowing at the same age as yours... But, if this is a single chicken with no companions, I would consider its high alert mode due to feeling its vulnerability).
Such 'alert' behavior is common in a wide variety of personality or character types, from nervous types (most commonly) to aggressive types.
Unfortunately, I generally do not find such birds to be keepers due to the exaggerated traits such chickens tend to have. It's fine to adopt such posture and behavior in response to relevant stimuli, but not to walk around in flight or fight mode nonstop, as I'm sure you can see it tends to indicate an excessively hyper mentality is present.
This generally does not result in a useful flock member, but rather one that is overly vicious or anxious and therefore trouble for you, itself, and any other flock members. Same thing as a dog walking around with its hackles up nonstop, more or less.
However since you've indicated this is a pet basically (if I've read your post right) good luck with it.
Best wishes.