What would be the best pulse program to obtain a NOESY spectrum with the best peak resolution and shortest acquisition time on a Bruker Avance IIIHD NMR spectrophotometer?
The best alternative for standard NOESY is probably the NOESYPHSW parameterset.
There is always a compromise between acquisition time and resolution, however, and if you want the highest possible resolution for some selected correlations you might want to look into the selective 1D versions. The "advanced NMR experiments" guide (the exact name depends a bit on the topspin version) has a step-by-step guide for setting up the experiments, or you can also use the automatic setup found in the acquisition tab under Go -> Advanced -> set up selective 1D experiments