I'm in San Antonio, TX. There is a difference between classic and antique plates. Classic plates are more just to look cool, no real benefits (annual registration or inspection still must be done) Antique plate on the other hand, have special rules. Plates cost around $55 and are good for 5 years. No annual inspection requirement but, by your word to DMV, all factory installed safety items must function (lights, seat belts, e-brake) and you must keep liability insurance on it. HERE IS THE KICKER!! Vehicles with antique plates CANNOT be used as daily transportation, only for car shows, parades, going to the repair shop or emergencies.
My 86 Monte Carlo had antique plates. It also had a 454 out of a 70's Chevy pick up, long tube headers and true dual exhaust with no cats and series 40 flowmasters. It did not have a computer or any emissions items. I drove it all the time but if someone with a badge asked me, I was on my way to a car show or I was on my way home from the auto shop.