Parts sources: Is there a single correct answer? I doubt it.
Familiarize yourself with, and get catelogs from, several parts sources. Mac's has a catalog, so does Larry's and Bird Nest. I've doen business with all three and recommend them. Another is Bob's Bird House, but I'm not sure if he has a catalog -- but I've done business and he's good.
There seems to be three parts categories -- new, repro, and used. Used parts -- some parts are ONLY available used. Certain trim, replacement doors, seats, etc. You can buy used parts from certain parts houses, and you can buy them from someone who happens to be parting out an old car to scrap. Check with Hammings Motor News, or forums such as this one. When someone says he's parting out a car, get in touch.
Repro parts can be scary. Some are well made while others are crap. If you're unsure of a specific part, ask others -- someone else may have had experience with that same part.
New parts may be NOS (in the box, but sitting on the shelf for 50 years), new in terms of Ford still making them, or parts made elsewhere and sold by outlets such as Napa. Most "hard parts", meaning engine, brake, and other parts that make the car go, are available at Napa, or other auto parts stores. These range from good to cheap. Napa is generally reputable; so are many local independent stores. The chain stores such as Advance seem to have improved, but you might still get some cheaper replacement made in China.
About all I can say is, use your discretion. Check with cruiser-friends to see who they use, and what experiences they have had. Then go with someone who has a favorable reputation.