Re: Won't run without choke
Car looks like it has had reasonably good care.
If it was mine, I would do the following to confirm if nothing else that things are working properly.
Check timing, plugs, points, gas flow to carburetor, all wiring, gas cap, (have you tried running with gas cap off?). Than I would remove carburetor and completely clean everything, making sure all passages are open including jets.
I think you have a couple of things going on. Nothing major, just a car that maybe has been sitting and/or has not seen much use in a while.
You need gas and spark, that’s it. I have seen similar problems in other Model A’s over the years.
Take a little time to make sure everything is right. One or two weak systems, everything goes down hill fast. Enjoy.