Clearly the OP is new to aviation, so I'll humor the questions. He doesn't know what he doesn't know.
Look at the acquisition, fixed, and hourly costs quoted above. If these are no big deal to you, sure go for it.
If you really want to fly it yourself, take lessons. You'll need to start with a piston single, but if money is no object (and you have the time and interest) you'll be able to advance quickly.
When you start talking about older jets, be aware that one reason they are "inexpensive" to buy is because they are not inexpensive to operate. For example, they are a lot less fuel efficient than more modern aircraft. There are other aircraft that would be more expensive to buy, but would be more reasonable to run on an hourly basis. Keep that in mind. The majority of costs in aviation are not the aircraft purchase, but rather operational and maintenance costs.
What is your annual budget and how many hours do you want to fly per year? What is your typical "mission" - ie. How far, how many people, how often? Do you really need to be the "captain" or single pilot, or would just getting some landings/stick time meet your needs?
The fancier the aircraft, the more it's insurance rules (rather than the FAA) that will dictate the experience/training required. If you don't care about having insurance, there is no law that you _have_ to have it - it's not like auto insurance. You can "self-insure" (ie "roll the dice") if you want. Keep in mind though that if nobody will insure you, they likely have a good reason based on their experience with similar pilots.