My 56 s88 sedans likes to stall out at stop signs and red lights after about 15 minutes of driving. I have to spray starter fluid during the initial crank and sometimes (rarely) have to spray some starting fluid to restart when it dies... I can turn the idle up one the carb and it runs okay and will stay cranked when the transmission kicks down to first. However, when I do this the idle is very high when in Park, but slow to just right when in gear. Also it jumps hard into drive or reverse coming from Park...

Ive been told carb, possible vapor lock (which im skeptical), Vacuum issues. The Jetaway trans will sometimes shift inconsistently and will not shirt to 4th gear (so Im thinking could possible be involved)

So looking for you advice. What are your thoughts and which should I start with?

 

You're going to have to go through the entire fuel delivery systems, one piece at a time. And yes, vacuum lines, too.

Start with rebuild kits for the carb, and fuel pump. Replace rubber hoses from the fuel tank on up.
When it's running, listen for hissing or sucking noises to find vacuum leaks.
When you are done, it should start from cold with one pump of the accelerator pedal if everything is right and tight.

 

Here's a thought: Before spending a DIME on parts you may or may not need, how about starting with some basic, free troubleshooting and diagnosis. The number one thing is to check for vacuum leaks, either deteriorated hoses or a loose carb. Check for proper choke functioning. Check for proper ignition function, especially timing and dwell. Check for fuel pump pressure.

Once you do that, you'll know where to spend your money on repairs.

 

I seriously doubt that the symptom you describe are caused by vapor lock.

They are more likely the result of vacuum or fuel delivery problems. When I had a similar circumstance I tracked it down to a faulty distributor vacuum advance.

 

I'm siding with the vacuum leak guys. Turning up the idle is just overcompensating for a leak.
I'm not familiar with a 56's vacuum layout, but does it also have a modulator valve for the transmission? That would explain the funky shifting. Either a vacuum leak to the mod valve or maybe a bad valve itself.
Follow the KISS principle before laying out any money for "possible" fixes.

 

I'm not familiar with a 56 either, but it really does sound like a vacuum leak. Do you have a PCV valve? Those have a bad habit of sticking and causing a hard-to-find leak. Once your car is started, spray light shots of carb cleaner around the intake area. If the engine speeds up at any point you have a vacuum leak. Track it down and fix the cheap stuff before you start throwing money at things that don't need it.