TechManual, IIRC, has intro dates which should give you an idea about the specialty weapons. Most generic weapons are pretty well spread out, with few notable noteworthies, such as the FWL's love of the LRM, Stiener's Gauss obsession, Davion's in-fiction love of all things Autocannon, and the Blood Spirits prediliction for the LRM-15 / ER Lg Laser deal.