Parts ARE available. Most collectors are like me who get approached from friends and neighbors who know of my interest and pull a "I'm cleaning out my barn" and offer parts for the effort to carry them off.
Ebay is a source for parts - at mostly reasonable prices. I say mostly since if you look for certain parts, you may find THAT PARTICULAR part is in demand and short supply. You may have to settle for something less than original or "as produced" by Ford for your particular vehicle.
The big dearth is "body parts" - especially on the coasts. A complete body is a treasured and valued thing nearer the coast. There are reproduction parts available even using the original molds to create them - but bring your wallet.
The nice thing about a Model A is that it typically has about half the number of parts that any modern car has.
And, you have to compete with the "rodders." While I have been to the "Race of Gentlemen" in NJ, and appreciate the vehicles "cobbled together" from pre 1937 parts, the tendency of a complete Model A is to turn into a "rod." Everyone hearkens back to their 1950s origins and tries to emulate their older brother who took what he had available and "souped it up." Today that generation frequently has the money and time and interest to try to exceed their older brother (or father) and all the material to do this is available for less than $10K.
At Epping NH flea market I have seen complete "barn fresh" Model As on the backs of car haulers being bought by someone YOU KNOW is creating yet another rod.
I have to restrain my critique as I guess that is preferable to the auto salvage guy who comes with a car hauler and leaves $200 in its place. Which is where it might have been otherwise.
As to what to get - try to get as complete as possible in an "original car." Barn-fresh can still be found. And this will give you a big advantage over trying to "assemble a car from parts."
I have the original "barn fresh" (avatar.) Also 60 percent of the next car (parts) Also 40 per cent of the next car (more parts) also "a whole bunch of parts left over I don't know what to do with."
The problem is those parts from the first that keep trying to convert themselves to the 2nd, 3rd, and 4th categories...
Joe K