You will be told how much the hold can take on your chosen aircraft and can upgrade if you feel more space is needed. This will generally be far more than that of a commercial airline. You may also need to upgrade if carrying things like golf clubs and skis. If travelling with a gun, you will need to provide a license and the gun and ammunition must be kept separate. It is then at the captain’s discretion whether it can be on board.
Though the early Lockheed Jetstar had four, most production business jets have two jet engines, mostly rear-mounted podded engine. If mounted below their low wing, it wouldn't allow sufficient engine clearance without a too long landing gear. The HondaJet is the exception with its over the wing engine pods. Dassault Falcon still builds three-engine models derived from the Falcon 50, and the very light jet market has seen several single-engine design concepts and the introduction of the Cirrus Vision SF50 in 2016.