You can use the city governor, but STILL manage your specialists manually (well, in some cases the governor will override your decisions, in those cases you have to turn him off).
For example, if you want an engineer specialist, turn off the governor, put the specialist into action, then turn on governor again. Usually he will respect your choice. Exceptions usually happen when you tell him to max food or production, in which case he will often put the specialist back to work on the fields
Generally, the choice of what specialists you want depends on your situation (big surprise). Normally, I wouldn't put a specialist to work before your city gets a reasonable size however, like 7 or 8.
To find the uses of the specialists, mouse over them (or look into the civilopedia). You want engineers or prophets to improve production (hammers), merchants or prophets for cash. Scientists for well, science

and artists to boost the cities cultural output.