I own a first generation Bonanza. It was built in 1953. But very few instructors have experience in a first generation Bonanza. They are unfamiliar with the operation and understanding of the electric prop, wobble pump operation, ever changing weight and balance, and the procedures regarding the pressure carb including how the fuel system works. Plus, this airplane has considerably lighter, faster responding flight controls compared to second and third generation Bonanzas. My airplane is IFR certified but using 20-40+ year old "steam gage" avionics including my "newest" avionic... a Garmin 250XL GPS. Far from a glass panel. So, it makes it considerably difficult to find an instructor that has experience in my airplane for a flight review. An instructor familiar with an A-36 equipped with a GTN 650 would not necessarily be knowledgeable on my V-tail D-35 with its Garmin 250XL.
I would also join a type club that supports the airplane you are considering for purchase. In my case, the American Bonanza Society is the gold standard of type clubs. They will direct you to a qualified CFI, if what you are considering is a Bonanza. But there are many excellent type clubs supporting various makes and models of airplanes. They are also invaluable when it comes to getting a pre-purchase inspection. Just because someone has an A&P license does not make them qualified to look over whatever you are considering. Once again, a type club will be your best friend when evaluating an airplane and/or instructor.
High performance, complex airplanes are easy to fly. But any in-attention to details can rapidly build into a series of events that can quickly become deadly. And there are many details. Airplanes are lousy classrooms. And no GA simulator can replicate the confines of a the cockpit nor the feel of heat, sweat, and being bounced around as one learns the art of flying.
High performance, complex airplanes have a different nature depending on how they are configured. Gear up they fly one way. gear down, they fly another way. Gear up, flaps down, they behave another way. Gear down, flaps down to full, they behave differently than gear down and only 10 degrees of flaps. So, one has much more to learn than just getting used to flying the airplane once it is up in cruise configuration. A first generation Bonanza has a very benign stall with gear down flaps up, flaps down and gear up, or clean with both flaps and gear up. But it has quite a pronounced stall and left wing drop with gear down and full down flaps. One has to make provision for those nuances of that particular type of airplane. Your instructor would need to be aware of all those characteristics.
Good luck in the learning curve to make good decisions regarding aircraft purchase and securing a qualified instructor you can personally work with. It can be done be done but make sure you get the knowledge you need to safely become both an aircraft owner and a safe pilot capable of using and enjoying all of the components that make up flying high performance, complex, retractable gear airplanes.
You can pick any instructor you would like under FAA Part 61 regulations. However, your airport may have a different say in the matter. If the airport has rules for commercial operators then your "independent" instructor may fall under the rules.
Per FAA Order 5190.6B, if you are a tenant in the airport and the airport receives Federal funding, airport management cannot prevent you from bringing in your own instructor from off-field.