Well, as a newbie, I can't really give you a good day in the life feel, as I'm still figuring it out myself. However, as to when DOM's are assigned, you know your plane and certificate when you're hired, but don't find out your domicile until you're almost finished with sim.

There's no pattern where newbies end up, it just depends on the month and is spread out pretty much over all the bases, except for LGA which takes about a year to hold.