Do the free checks first, take out the dv and block the hole, and also the vac pipe to it, if it now idles you've found your problem, it defo as said sounds like a air leak leaning mixture out or a duff iscv, idle speed control valve, ie not opening enough and admitting enough air to allow engine to run.
Usually if it's due to being very lean the engine will be a bit juddery on idle as well as cutting out, but should be cheap easy fix.
tabetha