After tailoring and taking your measurements, choosing fabrics and style, find out what the turnaround time is. For popular tailors, this can go up to 4 weeks. But in general, expect to wait about 2 - 3 weeks.
Ensure your tailor does alterations after the first fitting.
Its a misconception that after taking your measurements, the shirts will fit perfectly. In most cases, it will not. Perhaps the biceps are too tight when you bend you arms, or the stomach area too flappy when you start slouching.
These are flaws that take a few days to appear, and you will have to bring back the shirt to the tailor for a nip tuck session. Maybe a quarter inch wider for the cuffs, 1 inch narrower for the chest, half inch wider for the arms. These minor adjustments cater for real life wearing of shirts.