When GAs go out to stake conferences, they scout for MP candidates. GAs scout in other forums too, like when they interact with Stake Presidencies over issues that come up (boundary changes, building problems, natural disasters, missionaries getting sent home, etc).

Stake presidents don't recommend MPs. You can see that in the handbook. It's in the chart of callings. However, when a GA recommends someone as a MP, that candidate's SP gets a questionaire that asks about health, family circumstances (including kids' ages) and whether the couple can easily step away from careers and come back into them 3Y later (or retire). There is no favored career, although I would say that an inordinate amount of church employees get called as MPs. That is probably for 2 reasons: (1) they get seen by and therefore recommended by GAs more often than your average member; (2) the missionary department and senior brethren in the Q12 and First Presidency don't need to worry about destroying their livelihoods with the call because their employer will take them back in some capacity.