The Five Specialist (yes, five!):
1. Taxmen: benefit = 2 gold, not subject to corruption, useful in corrupt cities when you're not researching
2. Scientist: benefit = 3 science, not subject to corruption, useful in corrupt cities when you're researching
3. Engineer: benefit = 2 shield to building improvements and wonders, not subject to corruption, useful in corrupt cities and cities without factories
4. Policemen: benefit = recovers 1 shield + 1 commerce from corruption, the recovered shield and commerce is then subject to multiplication from improvement. The exact benefit from policemen depend on the number of improvement in the city. The policemen is useful in core, developed cities, that don't need the shields generated from specialist # 5.
5. Mine over that irrigated tile, get rid of that specialist: benefit = 2 shields, which is then multiplied by the factory and the powerplant to 4 shields, useful in core cities with factories that need the shield (to reach the shield break point of what ever it is that you're building).
SUMMERY
Taxmen: always 2 gold
Scientist: always 3 science
Engineer: always 2 shields (when building improvements and wonders)
Policemen: (almost always) 1 shield + 1 gold, up to 2.5 shield and 2.5 gold with nuke plant, stock exchange or research lab
Mining: always 2 shields, usually 4, up to 5 shields with nuke plant, though the shields are subject to corruption.
Basically, if the city is corrupt or undeveloped, chose between taxmen, scientist or engineer. For the core city, chose between policemen and mining, depending on the need for shield.