Generally speaking, most consider a "true" muscle car to be an intermediate size car with a large/high performance displacement engine, usually over 380 cid, and built between 1964 and 1972. However, the term is open to discretion, as there are cars that by definition, are not "muscle cars" that tend to get included, for example, the Camaro, Mustang, 'Cuda, and all the other Pony Cars. I have also seen sports cars, like the Corvette and Cobra included (Muscle Car Review 100 Fastest Muscle Cars). The you have all the full size cars that tend to get included on some lists, like the Z11 Impala and the Max Wedge Plymouths.
As far as which was was first, gets a bit muddy there. By definition, that title should go to the 1964 GTO (there was no '63), but then again, some consider the '57 300 the "first". Others consider the '55 Chevrolet V8. Then, going further back, I have heard of some folks considering the 1932 Ford Model 18 as the first muscle car, usually citing Clyde Barrows preference for using them as getaway cars because of their superior speed to other low priced cars. I've even seen Deusenbergs put on some lists.