Thanks for the interest. Those are good questions, and I'll elaborate on a lot more actually.
I'm not sure how they're recruited in MIB, but they're definitely not cloned, neither do people get the positions passed down, but recommendations are common. For field agents, like the enforcers and detectives, they would already have to be a professional in a similar field. No common police officer, but people who have dealt with top secret clearances, like former government employees. Jobs would most likely be offered to people who already work in the more classified work of the CIA, US Dept. of State, or the DoD (or private contractors); jobs that would already require extensive background investigations, and top security clearances. People with families are just as viable candidates, provided the prospective employees would not be able to tell any sensitive information about their work to even their closest loved ones.
Accountants and human resources would also probably come from some kind of reputable background, and there would be a few people who would be recruited with non-government backgrounds, like computer scientists, doctors, forensics, and researchers -- even PR. The agency is very human, and most of the RP aside from the explicitly sci-fi parts will be handled realistically. Naturally, all employees would be subject to intense background investigations, medical examinations, data mining and surveillance (without consent), and a polygraph test.
There are no memory wiping sticks or stuff like that. Every employee goes through weekly psychiatric evaluations as well due to the sensitive nature of their job, which may play its own important part. Everyone that was recruited was offered the job, some former employees work in higher positions within other agencies, and often do most of the scouting for them when they are contacted about vacancies or recommend exceptional candidates in an applicable field. Enforcers have to be trained killers, as that is essentially their job, to track down and kill roaches, while detectives or investigators may not have to kill roaches themselves, they will probably see it happen before their eyes more than once, it's less likely this kind of information gets relayed in such detail back to the offices and labs.

Originally Posted by
Naril
This is interesting. So the overarching message of the DSI is that these mutants/offworlders/whatever are Bad Guys, but that may not necessarily be the case (hence agents sympathising with them), and there may be some kind of ~rebel against the system~ thing going on later on down the line? Also, where do agents for the DSI come from? Are they recruited like the Men in Black? Cloned? Handed down from generation to generation, with Harold Reportfiler III handing down his job to Harold Reportfiler IV?
Yeah, exactly. The DSI was supposedly drafted by an international meeting of superpowers in order to address the rising problems of these paranormal activities. But it seems to be, at least to the enforcers who actually get to see it on the field, that the policy is that there are no negotiations or any actual solving into any criminal motives, just an extermination. Collateral damage is the excuse when a civilian becomes compromised by a roach, in which case if the human can be, they will be captured and placed under mental care of a special psychological unit within the DSI, otherwise enforcers are licensed to kill at their discretion. To ensure that there aren't defectors or sympathizers, the psychiatric evaluations work directly with internal affairs.
There is a sub-conflict with an underground movement(s) for roaches trying to assimilate into normal human life, and a more violent movement(s) for those who are simply seeking vengeance or retribution. But from the way enforcers operate, there seems to be a clear understanding at the top of the DSI of what roaches really are or where they are coming from, an understanding that is not shared with most employees. In the case that a roach cannot be killed by conventional means, or that they are in a public area and must be arrested to maintain appearances, field agents are equipped with some kind of syringe that makes use of some unique medical technology -- it appears to nullify the super human capabilities of roaches, thus the implication that the people at the top do know a lot more about these roaches despite their one sided approach to handling them. This is also why some employees question their work, when they realize that the danger can be forcefully extracted from a roach, yet still their existence is to be wiped off the face of the planet, causing more questions about their real mission.
On the note of field agents, sometimes they face opposition from other law enforcement and organizations, as the DSI's credibility isn't so easily verifiable, considering that no other government programs have any recorded information, so those in the field are outfitted with various credentials, usually as paramilitary operators, since the very existence of DSI is a secret of its own.
Becoming a sympathizer or something of that sort is definitely one of the biggest risks next to injuries in the field. Any underground movement would be another priority of the DSI to be taken care of, and anyone known, including civilians, to be associated with it would be listed as an international terrorist on other law enforcement or public databases.