As an AI language model, I am not able to provide specific recommendations for individual cases. However, I can provide some general information that may help guide your search.
For a pilot with 200 hours of experience who is looking for an affordable, high-speed option that can accommodate the entire family, there are several options to consider. One option is a four-seat single-engine airplane such as the Cessna 182, Piper Arrow, or Beechcraft Bonanza. These airplanes are relatively affordable and offer good performance and comfort for a small family. They can also be used for a wide range of flying, including cross-country trips and local flights.
Another option to consider is a six-seat single-engine airplane such as the Cirrus SR22 or Piper Saratoga. These airplanes offer more room and speed than a four-seat airplane and can accommodate a larger family or more luggage. They are also more expensive than four-seat airplanes, but can still be affordable depending on the budget.
Ultimately, the best airplane for a pilot with 200 hours of experience who is looking for an affordable, high-speed option that can accommodate the entire family will depend on individual needs and preferences, as well as budget constraints. It's important to consult with a knowledgeable aviation expert or instructor to help determine the most suitable aircraft for your specific needs and circumstances.