The most economical option is chartering, which doesn't require any cash upfront (other than a deposit) through companies like Tradewind, Sentient, and Solairus, (which we took home from North Carolina). Of course, there are the old standbys like NetJets and Marquis, who sell fractional ownership (like 1/16th) of a single jet for upwards of $100K. One step down from that, pricewise, is the jet card, where you buy a set amount of hours from a company like Nicholas or Private Jet Services, and can use those hours for different planes. Then there are membership models like WheelsUp, where you pay $17,500 as an initiation fee to fly in their fleet, and then a $8,500 annual dues fee starting the second year. It's like a country club—only you're guaranteed access to a KingAir350i or Citation Excel / XLS instead of a golf course.
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.