Time for a Long block?
I wouldn't jump into a long block based on what one mechanic said. Ditto post #4, things don't quite add up. Free test - turn the engine over by hand by tugging on the fan belt (key in your pocket, pull plug wire off coil to be safe). If you feel 3 strong "air springs" resist you per crank revolution (chalk mark) and hear them hiss down, the "no compression" data is bogus. Kick over a motorcycle and you will understand.
Bad rings cause blue smoke out the exhaust under full throttle (have someone follow you), plus excessive oil consumption. Bad valves is a "head job", not a new long-block. Bad valve guides or seals is much smoke as you drive away after sitting at a stop light for 5 min. Often just replacing worn rubber umbrellas on the valves fixes it, which you can do w/ the head on the engine.
Stuttering from a stop has little to do w/ bad compression and more to do w/ fuel. My 1969 slant ran like that for decades, particularly when hot, and I feared stalling at every red light so often had to goose the throttle. I suspected fuel, but 3 rebuilt Holley carbs didn't change it, nor did several valve jobs, and no mechanic could diagnose it. Finally, after it still did it after a complete rebuilt long block, I bought a 4th 1920 and it purred like a kitten. Unbelievable change. If you have a Holley 1920, there are many bad rebuilt ones. The sealed metering blocks clog and most rebuilders don't touch that part.