A properly restored A will drive like it came from the factory.
From the factory they would run 55+ MPH, get over 20 MPG, could be abused, and stopped very good for the tires. You should expect 50,000 miles out of a properly babbitted engine that was returned to Ford specs.
A well restored car can do the above, so a properly restored car should have no problems based on my experience.
Usually you can find a car that looks nice with the mechanicals a mixture of well restored, repro, and used parts. It is fairly expensive to properly restore the chassis back to factory accuracy as Ford was much more accurate they most can believe.
You need to find out who did what to the car and what method they used. An engine built up by the guys friend in the next county is not likely to survive a long as one done by a major engine shop with a reputation. If they say they put used parts in the brakes then do not expect much from them. Budget in the cost of fixing the chassis in your purchase price.
Just because it is a car from a "professional" restorer or a museum does not mean it is a good car. One local guy bought a professionally restored car and spent another few thousand making it safe and reliable.
Buying a done car is usually less money then trying to restore one. Watch your wallet as it is too easy getting significantly upside down with your money. Nothing like having $40,000 in a $12,000 car.
Lastly,
Make sure you can drive the car and like the fit. The Model A is small and some bodies are a bad fit on you. I am very tall and I am not compatible with 28-29 open pickup trucks. I can not physically drive them as I have trouble with the peddles.
