What should I check first

My '88 did the same thing many years ago. Your symptoms sound exactly the same. When the pickup screen in the fuel tank collapses or becomes plugged, the engine will run fine when the least fuel is being pumped which is during acceleration and cruising. It will starve for fuel PRESSURE when the largest volume is being pumped which is during coasting.

The first clue is it will likely run okay for the first five to fifteen minutes. A second clue can be found by disconnecting the vacuum hose from the fuel pressure regulator on the fuel rail on the engine, and plugging it. You'll get black smoke from the tail pipe, but the engine should run without starving for fuel. If it does, suspect that pickup screen.