To answer the question is a Mooney M20 difficult to fly, the answer is no, it is not. They do demand a smooth roundout and touchdown due to the stiff suspension on the trailing link gear. As other have pointed out, it’s a complex airplane and is going to be more expensive to maintain and insure for a neophyte pilot.
A major difficulty for a new pilot to cope with is the speeds and capabilities of the airplane. Expect a early model M20 to be about 50% faster than a Cessna 172 and modern turbocharged variants like the M20M Bravo and M20T Acclaim are capable in excess of 200 KTAS and operations as high as FL250. They have more systems to operate and handle and offer a considerably larger flight envelope than a typical trainer like a PA-28 does. This greatly increases your capability for using the aircraft for travel but it can also be a rope long enough to hang yourself with if you’re not careful.
Low time pilots are typically deterred from Mooneys for these reasons. Similar to a new motorcyclist transitioning onto a 1000cc sport bikes, a low time pilot can get into one of these complex, high performance birds but needs to be aware of the risks in their operation. If you intend to do primary flight training in one of these airplanes, while it can be done, It will inevitably be more difficult and costly to do so both for getting the aircraft flight time, as well as the insurance demands for a new pilot. Insurance companies may will set a minimum hours of dual time required before they will even let you solo the airplane and may demand that you obtain an instrument rating before even being allowed to fly the airplane solo as a private pilot.
Here’s what I would do: find a decent flight school with a nice 152 or 172 and do your primary flight training and that to get your PPL. Next obtain an instrument rating on your private pilot certificate, and then finally look into buying a Mooney or similar high-performance bird. If you do select a Mooney or Cirrus, or similar aircraft, seek professional instruction from the factory and schedule recurrent training with a factory instructor pilot.
In the time that it takes you to complete your private pilot certificate and instrument rating, I would also be researching Mooneys for a year or so and befriend a qualified mechanics who has experience in the M20 airframe. You will need to employ him to obtain a pre-by inspection on one of these aircraft and it’s very useful to do so to avoid ending up with an airplane that has a lot of maintenance issues. It will also help you learn about the Mooney airframe and some of the things that can go wrong with it.