Mustangs are pretty simple to keep on the road; the engines are a lot simpler than what you'll find in modern computerized cars.
But these cars are 30-35 years old, and things do break, wear out, fail inexplicably. And modern repair shops are geared up for the modern electronic gizmos. Not all mechanics today are familiar with older cars, so some problems can be tough to troubleshoot. You don't have to be a mechanic to own a Mustang, but a willingness to get your hands dirty and learn the basics sure helps.
Maintenance schedule is pretty much the same as for all cars, though---regular oil changes and tune ups (which can be handled by most auto shops).
Gas mileage for a stock, 6-cylinder Mustang is probably somewhere in the mid to high teens (16, 17, 18 mpg). V8s get somewhat less---14, 15, 16 mpg. Some people claim as high as 18-20 even for their V8s, though. Depends on maintenance, engine tuning and driving habits. You can use regular-grade gas in all Mustang engines except the High Performance (HiPo) models, which require premium.
Don't worry about lead additives. While older engines were designed for leaded gas, they work just fine with unleaded under all but the most extreme conditions (heavy loads for extended periods). And if the engine has had a valve job since the mid-80s, it probably has hardened valve seats, which are designed for unleaded gas.
Most parts are readily available, at least for the 1965-66 models. Some parts for later models (in the world of vintage Mustangs, "later model" means 67-73) are a bit more difficult to come by, but they can be found.
As for cost, depends on the part and on whether you will accept a reproduction part, or insist on a Ford original. Repros are less expensive but often do not fit exactly; originals are sometimes hard to find and can be quite expensive. A few parts simply cannot be bought new at any price; they have to come from a "parts" car or junkyard.
See also these message exchanges on the Vintage Mustang Forum:
submitted by a65ragtop