1988 Sable hesitates or stalls after a complete stop

A few things come to mind when you describe these symptoms;
The fact that the idle has issue when you brake could be related to the power brake bosster.
To test it, do the following;
Without the car running, pump the brake pedal until it is firm and hold it. Start the car and the pedal should drop away slowly about an inch or two. As long as it drops is is probably fine.
Otherwise the is something going on with dead stop throttle response.
This is probably a fuel management or supply issue. It could also be the spark plugs and wires, etc. As they will fail after time even with low mileage.
A few things to check to see if the Idle Air Control valve, (IACV), is the problem. It controls idle as extra load is put on the engine. If the car has worse performance and idle when you turn on the A/C, headlights and other accesories, this clould be an issue.
Otherwise the injectors could be dirty and certainly the throttle body and intake manifold. The thing about cleaning the throttle body by just spraying cleaner down the throat is that the residue gets washed down into ports like the IACV and clogs them up. Also, very few injectr cleaner =s on the market are very affective. The reason being is that people will use them without enough gas and then damage the motr which leads to a liablity issue.
Look for a product called, BG44K. You will have to go to a dealership or service station to get it. Run a can or two of it and then be prepared to change the oil as it works so well that it makes it dirty with the removed deposits.
If problems persit. You may have to remove the IACV and the throttle body to clean them out. Also, inspect the plugs and plug wires. If they are the originals, they do need replacing as they are too old to not have deteriorated.

It sounds like the brake booster is failing. It should drop under foot noticeibly. I think the real diagnostic sypmtom you discovered is the, "wooshing", sound made when the brakes are depressed.
How far does the pedal travel when pressed?
Also, does the brake pedal get firm before starting the car if you pump it a few times?
There might be a combination of problems.
The site has picked up Summit Stock Replacement parts, which is one of the best and oldest parts supply shops around. They are performanced based, but they have stock replacement parts from good remanufacturers and nobody beats their customer service.
It is $50.95 with a $25.00 core charge refundable upon return of your old booster. The nice thing about Summit is they will provide you with a UPS return package that UPS will pick up at your door.
Here is the link;
http://www.summitracing.com/parts/AAZ-54-74300/
You will also get a cool catalog in the shipment to drool over.
Brakes are important and there are enough odd things to justify replacing the booster.
Let me know how things go and if you need anything.