You may or may not need a Private Investigators license. Also Process Servers & Bounty Hunters.
Most areas have no licensing requirements. Check out the latest Bail Enforcement Agent (Bounty Hunter) laws in this forum.
You may not need a gun permit as a private investigator. Only 5% of all PI's have a need for a conceal weapon, as most assignments are non-confrontational and are undercover. Still, this new forum will explore the state-by-state requirements (if any) for your consideration.