Do you need type ratings for private flying?
In addition to a type rating, you cannot fly a 737 without a commercial pilot's license and 1,200 flight hours. Further, your flight and maintenance operation must be certificated by the FAA. You'll need FAA approved opspecs, flight manuals, pilot training and testing, a drug test program, hazmat program, a designated safety manager, and more.

Aircraft with 20 or more passenger seats, or 6,000 lbs payload capacity must be either flown under Part 121 air carrier rules or else they fall under Part 125 regulation. Except for limited circumstances, they cannot be operated under Part 91 (exceptions fall under Subpart F). Because your party isn't a training flight, you don't own the plane, it isn't a sports team, etc., you are under Part 125.

Once the aircraft is large enough, there is no longer a distinction between private and commercial operation, Part 125 covers commercial operations short of common carriage. Even if you're operating an aircraft privately, you have to comply with commercial level safety requirements.