Buying a used plane is not something you want to do in a vacuum; there’s too much tribal knowledge. Early in the process, start building a network of people that are willing to give you dispassionate advice. There’s a good chance you already have at least a budding network in the form of friends and CFIs, but you want to think more formally about this as your search gets serious. Some useful people to contact:
If your flight school has a good maintenance department, get a cell number for someone on their staff. Even a small school will do huge amounts of work on planes every year and have a good perspective on the long-term realities of plane care. This means that they’ll be able to answer questions like “I’m looking at a 182RG. How much of a premium will I pay for the retractable?” or “What is the difference between a wet wing and fuel bladder?”. Importantly, their answers will draw from actual data and experience rather than vague water cooler talk. If a random pilot says “RGs are completely fine; their gear isn’t more expensive to maintain” that means they heard someone say that once. If a flight school mechanic says that, this means that over years of maintaining multiple RGs they haven’t found any large difference relative to fixed gears.
Hopefully you have a good relationship with at least one or two CFIs. They’re good to talk to about what it’s like to fly different aircraft. Even if a CFI spends all of their time instructing in a few flight school 172SPs, they probably still have a broad base of experience from their own training, side work as a ferry or corporate pilot and from instruction in owner aircraft. If you’re wondering how a specific model flies, or what to expect from transition training, or real world performance vs book numbers, ask your CFI.
You’ll need insurance, which means you’ll need an insurance broker. A good starting point is the AOPA. If you give them a call and describe your situation they can connect you with a good broker and give you approximate quotes. This is important because insurance costs can have a huge impact on a plane’s affordability. Suppose you’re leaning towards a Cessna 180. Tailwheel planes tend to be more expensive to insure; better to learn that right away than after you’ve become attached to a specific tail number.
Once you have a plane you’ll need to park it somewhere. Different airports have huge variation in the quality of the FBOs, the on-field maintenance, costs to owners, and convenience. Make friends with some local pilots; they’ll have invaluable insight you can’t gain just from getting a tiedown quote. They can also provide the right contacts to help get a tiedown or hangar. At busy airports, it can be tough to get a parking spot quickly if you don’t have some contacts.
Don’t be shy about asking people for help or information. Most pilots and people connected to aviation love general aviation and want to get more people involved. If someone asks me 1000 questions about owning a plane, I don’t hear 1000 annoying questions but rather 1000 opportunities to help someone fully immerse themselves in the world of flying. That attitude is nearly universal; when shopping around I asked many people dozens of questions. Everyone seemed happy to help and their assistance was invaluable.