Canon points
Normal journal canon: Just before the first Boondock Saints movie. The plan is to start to play through the brothers' timeline through the first movie, the gap inbetween, then onto the second and so on...
However, this is flexible and the mun is open to playing bendytime to fit other muses' posts/moods/running with inspiration when it hits.
AU Canon: Connor's a Da! Played with his daughter: Morgan.
not_yet_sainted (child Morgan) and
angel_not_saint (adult Morgan). Other muses are free to step in sws, etc, aimed for Morgan. Connor's mun is rarely ever exclusive about who plays in her games.
Love Hotel: Dropping Connor into the hotel somewhere mid-first movie, so he's familiar with most of his canon mates that might stumble over him, (maybe literally). Once again, this is flexible if need be.
Sexuality
Have a Connor that may be a little more on the gay side than he'd ever like to admit. He blames his fucked up mun. Women like him and he's not dumb enough to say no when they offer, but confession is mostly focused on what he'd like to be doing with guys. Though, he doesn't seem to be suffering that good old Catholic guilt as much as he should, just enough that he won't admit it to Murphy.
RP-wise, particularly for
the_love_hotel, there's little the mun is against playing, scat being the only thing that instantly squicks her and Connor. (There may be things that Connor objects to, but the mun doesn't... trial and error here...)
Obviously, incest is going to crop up from time to time. Or more often than that. It probably goes without saying...