Thomas,
Welcome. Sounds like a great ride! Give us more info on the car...auto/manual, engine, mileage, etc, and a picture or two!! We love to drool over other guys and gals rides.
What look to you wanna achieve? Complete stock resto, or modified stock, or total custom job? Do you know? If you wanna stay stock.....don't remove anything you do not already have a better looking or better functioning replacement for!!! Original parts for a '66 are rarer than a raw steak. Especially, don't toss original parts, even if you can't use them. They'll sell on E-Bay and help finance your mods!
What is your definition of a "clean interior"? Yes, there are many methods that work well to clean and restore tired, dirty, old parts. Those methods are about as varied as the guy doing the work, but not quite. It all depends on the part being restored, the material it is made out of, the type of dirt or restore needed.
You've come to the right place to get some real good advice. Be patient, and ask specific questions, giving a whole lot of background info (even if it seems too mundane to you). Remember, we can't read your mind; but we want to help you succeed.
You also might want to stop by the
Classic Mustangs forum and introduce yourself to those guys and gals. No sense in reinventing the wheel. They'll have been where you are today with the exact same vehicle. Might have parts for ya too.
Good luck. Hope to hear from you real soon.
Help With 66' interior 
