To the extent that ChrisH hasn't been scared away permanently (lol), I offer the following suggestions:
I commend you on your caution moving forward into uncharted territory (for you). Unfortunately, the more common scenario is a novice Mustang enthusiast comes here after buying a car off the internet sight unseen and quickly discovering that he/she is the proud new owner of a rolling piece of iron oxide held together with gallons of Bondo, duct tape, baling wire, and bungee cords. To conform the obvious, the Vintage car hobby does have some dishonest people lurking around so trust your own eyes when looking at a possible purchase. Knowledge is power when it comes to buying ANY 50+ year old car. As indicated by others in this thread, the most expensive mistake is not realizing that major structural rust (both visible and hidden) can take a wheelbarrow of money to fix properly. I have seen some cars that are so badly rotted that even if the asking price was "free" it would still be a bad deal. Being massively upside down financially in a car can seriously detract from the many pleasures found in the vintage car hobby.
The next thing to consider is that paying someone else to repair and maintain your car can elevate the cost of ownership to dizzying levels very quickly. Many folks here turn their own wrenches to keep maintenance costs down. Fortunately if you have the curiosity, access to a work-space, time, tools, and determination, you might surprise yourself with your own abilities as you learn the ropes of working on cars that come from the Fred Flintstone era of automotive electronics (LOL), as many here have done before you.
The common wisdom around here tends to favor the idea of buying the best car you can afford that otherwise meets your criteria. This advice is based upon the proven fact that a "done" car can usually be bought for far less than the cost of buying a fixer-upper and spending the time and money to bring it up to the same quality level as the "done" car. Being able to drive your car on day one has its benefits too. A basket case project car is generally not the best choice for a first venture into vintage car ownership.
Attending local car shows, Cruise Ins, and Cars and Coffee events (wherever it is you live?) will give you an opportunity to talk with other Mustang enthusiasts and learn about the Vintage Mustang opportunities and resources in your area. If this forum is any indication, many Vintage Mustang folks are friendly and helpful when it comes to sharing knowledge and resources. In the 19 years I have been involved with Vintage Mustangs, I have found this hobby is more about the people than the cars. I have met people from all over the US as well as Europe and Australia, many of whom I now consider friends.
Circling back to the original question, the '66 Coupe linked to your initial post looks like a nice car. If that car was for sale out here in NorCal, I would say the asking price is at the upper end of the price range but, if it is as solid as it appears, it could be a good buy. In any event, a pre-purchase inspection by someone knowledgeable and honest is a must. Post your general location. Perhaps there is VMF member local to you that might have a spare couple of hours to help out the new guy/gal.
Good luck with your search, proceed with patience and let us know what you find.