You have no idea what a manager does do you. Managers never work, and rarely know more the a general outline of what their underlings do. What they do do is yell at the little people; siphon off their self respect, and keep it in little vials, and act randomly. The higher up the chain of command, the less intelligent, less skilled, and more clueless (but higher paid).
I find DF to be a near perfect representation of real world management. At least, as long as I don't force my managers to be useful. I had one that was my entire military for several years, until she drowned after walking on a frozen pond, that unfroze while she was on it. It was just as well; I had a well trained real military at that point.
My bare essentials are this:
2 miners
2 masons
1 Mechanic, farmer, brewer, cook, stone crafts, bone carving, architect, carpenter, appraiser
I usually don't bother with engraving, as I can easily have it built up quickly. Woodcutting is dependent on the map; I almost always carry an axe though. I like having two masons because early on I have a need for a lot of furniture like doors.
I have played with all starting 7 as miners, which really helps dig out my initial antechamber quickly (which serves well as an interim stockpile until I get the fortress proper started). I don't bother with smiths because I never know if I'll have ore to start a metal industry. I'll relay on worked leather and cloth (imported, because I'm too lazy to start a farm for that stuff and process it all) and stone to trade for needed stuff like weapons.