A public charter is one in which a tour operator rents the aircraft and advertises and sells seats to members of the public, either directly or through a travel agent. In the case of public charters, the flight must be filed with the U.S. Department of Transportation, and the tour operator must supply a charter prospectus. The tour operator also must assume a legal responsibility to provide the transportation service, and must abide by DOT requirements for the protection of the clients' money. Public charters often operate only seasonally, and are often sold as part of a vacation package deal, although spare seats may be offered at bargain prices.
JetSuite is one of several private aviation companies attempting to make private jet flying accessible to travelers who aren’t part of the billionaire or even millionaire set. In many cases, these companies such as Blade and JetSmarter, are able to offer flights at appealing prices because the trips are shared with a small group of other passengers. While this may not be private flying in the vein of having an entire plane to yourself, travelers fly in and out of small, private airports where they usually don’t have to deal with the Transportation Security Administration and can arrive just five to 15 minutes before their departure time.
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.