The description suggests a choke problem as a first place to look.

In and around that era, it was common for (US) cars to use a "rapid unloader" of one sort or another that forced the choke open rather quickly, sometimes before the engine warmed up enough to run well - especially at idle at the first few stops. There were a couple of methods but a common one was to apply a bit of manifold vacuum "suck" to help the choke plate to the open position as soon as the engine was turning fast enough.

If it starts, the choke probably is closing sufficiently when cold, but may be "hanging open" when rpm goes down and some choke effect is still needed, so a bit of cleaning in the choke area might be helpful. This should not require removal or disassembly of the carbureter unless things are incredibly gunked up.

A fairly high-maintenance item on cars of that era was the PCV (Positive Crankcase Ventilation) valve, that usually sticks into the top of the valve cover to allow vapors from the crankcase to be sucked back into the intake manifold and burned. The valve is supposed to open and close in response to intake manifold suction, and if it sticks open it can make the mixture "excessively rich" at idle, when your stall is occuring. Replacement of the PCV Valve at regular intervals was usually recommended in that era, but is more of an "as needed" thing with more recent vehicles. (Other things have been redesigned to reduce the amount of crankcase vapor the valve has to handle - they say.)

If you can access it easily, a PCV Valve replacement should be easily done, the valve shouldn't be terribly expensive, and it's probably overdue if you haven't had regular service on the car, although it's not a "sure fix" for you present problem.

Your vehicle probably also has an EGR (Exhaust Gas Recirculation) system that feeds exhaust gas back into the intake to "final burn" the hydrocarbons out of the exhaust. (The addition of a bit of exhaust also makes the mixture "look richer" and allows leaner inlet fuel mix without knock/preignition etc.) There were numerous different systems, when/where they were used varies with which "market" the car was built for, and I have no reference sources to check what/which/ifany may have been on yours. Unless you're at least "semi-skilled" at maintenance or "obsessively curious" most maintenance of these systems probably is best performed by a competent shop ("competent" and "shop" used together are not always a non-sequitor, but caution advised)

When poor performance after sitting for a time occurs, and goes away after the engine runs for a while, a possible suspect is "weak electricals" but isolating this kind of problem can be difficult. What happens - sometimes - is that insulation develops cracks or porosity that allows moisture to penetrate "to the wire inside." Surface moisture allows "short circuiting" to unintended places - especially of high voltages in the ignition system, so things don't work well when you start up. When the surface moisture is evaporated, the "short" disappears, but this doesn't mean the absorbed/adsorbed moisture within the deteriorated wire/part is necessarily "boiled out." (An extraneous "wire" doesn't hurt a thing as long as it's not connected to something on the other end.) The condition can reoccur after fairly short times without use, since the internal moisture is still there, and only a very small amount of external/surface "dew" (usually not visible) re-establishes the fault condition.

An "experienced but not too fussy" mechanic might try spraying the ignition wire, plugs, and distributor cap with WD40 (a pretty-good, quick "drying agent") before the first startup to see if the problem is solved temporarily, but the only real fix is to replace the affected parts. (Note that excessive and repeated use of WD40 can cause deterioration of some insulating materials, although the amounts required for a quick look shouldn't be harmful.)

Mostly random thoughts here. Hands-on is the only way to be sure what's going on.

John