[tsunade666]

System....

well probably first Butei.

Butei (武装探偵, Busou Tantei, lit. "Armed Detective"), is a national qualification created to combat the worsening crime rate. The Butei are allowed to bear arms and arrest people. They'll take on any job for money, so long as it falls within the "Butei Law"

Butei Law Articles

Butei Law article 1: Believe in your comrades and help each other.
Butei Law article 2: You must fulfill the contract in the commission.
Butei Law article 3: You must become stronger. But above all, you must support justice.
Butei Law article 4: A Butei must learn to become independent. You can not help him if he does not request it.
Butei Law article 5: Be as fast as a gust of wind. Butei must win in one blow.
Butei Law article 6: Reflect by yourself, act by yourself.
Butei Law article 7: Be ready with pessimism. Act with optimism.
Butei Law article 8: Your mission must be resolved completely
Butei Law article 9: Regardless of the situation, a Butei cannot kill.

Butei Charter Articles

Butei Charter article 1: Believe in your comrades and help each other.
Butei Charter article 2: You must fulfill the contract in the commission.
Butei Charter article 3: You must become stronger. But above all, you must support justice.
Butei Charter article 4: A Butei must learn to become independent. You can not help him if he does not request it.
Butei Charter article 5: Be as fast as a gust of wind. Butei must win in one blow.
Butei Charter article 6: Reflect by yourself, act by yourself.
Butei Charter article 7: Be ready with pessimism. Act with optimism.
Butei Charter article 8: Your mission must be resolved completely
Butei Charter article 9: Launch out to the world. Co-operate with others, not differentiating between race or nationality.
Butei Charter article 10: Do not give up. Butei must not give up for any reason.

Additional Information

Assault 「強襲科」 - They uses handgun, swords and other weapons to perform melee combats in operations. Characters that fall under this department: Aria H. Kanzaki, Ryou Shiranui.
Snipe 「狙撃科」 - Their expertise lie in assisting members from long range distance by using sniping weapons. Characters that fall under this department: Reki.
Lezzad 「諜報科」 - In charge of making criminal organization intelligence report. They are also involved in the construction and destruction strategies. Characters that fall under this department: Hina Fuuma.
Dagula 「尋問科」 - In charge of interrogating captured criminals.
Inquesta 「探偵科」 - In charge of investigation in applying detective and reasoning skill to analyze informations. Characters that fall under this department: Kinji Tohyama, Riko Mine.
Repier 「鑑識科」 - Similar to forensics. In charge of scientifically testing proofs and use scientific devices to search for clues in crime scenes.
Amdo 「装備科」 - In charge of supplying, customizing and the maintenance of Butei equipments. Characters that fall under this department: Aya Hiraga.
Logi 「車輌科」 - In charge of piloting any kind of transportation means (land, sea or aerial transportation). Characters that fall under this department: Gouki Mutou.
Connect 「通信科」 - In charge of providing information as a backup using communication device. Characters that fall under this department: Misaki Nakasochira.
Informa 「情報科」 - In charge of compiling and sorting informations using information processing equipments. Characters that fall under this department: Jeanne D'Arc.
Medica 「衛生科」 - In charge of medical care during Butei activity or rescue operation.
Ambulace 「救護科」 - They serve in Butei hospitals. In charge of educating future doctors. These people had gained sufficient experience from rescue operations.
SSR 「超能力捜査研究所」 - SSR stands for Supernatural Searching Research. People under these course have supernatural ablities. In charge of supernatural or psychological crime investigation. Characters that fall under this department: Shirayuki Hotogi.
CVR 「特殊捜査研究科」 - CVR stands for Civetta Reseach. Only girls with exceptional beauty can enter this course. Under special condition, they use their physical charm to apprehend criminals.
Masters 「教務科」 - The faculty members of Butei School. Characters that fall under this department: Tsuzuri Umeko (Dagula), Sayanaki Tooru (Ambulace), Ranbyou (Assault), Nangou (Snipe), Chan Wu (Lezzad).

The next part are spoilers

Spoiler for info setting:

Aside from what division or more like class you want to enter. the basic are the fighting style. From different martial arts of close quarter combat to armed combat.
Butei aren't limited to what weapons to use though it's important to use a suitable weapon to the user. The use of blades for close quarter and handguns/pistol for mid-range and rifle for long range. Heavy armaments are allowed two as long as you can use it. Shirayuki uses M60-HMG and she know how to use it.

Aside from combat style and weapons the next thing are probably if your a butei or a super butei.

Super butei or choutei are the magic or ability users or beyond abnormal butei. This people need special kind of cuffs to deal with them. The specialize cuffs prevent them from using the ability or magic.

The other important is

Irokane (イロカネ Lit. Coloured Metal) is a metal with supernatural attributes. It is known as (超常世界の核物質 Lit. Core of the Supernatural World.)
Irokane...is something that makes all magic look like child's play, an enormous, colossal material that is filled with supernatural power.

It's a special rare metal that allows a butei to become a choutei. So even if your natural born ability user by using this metal you can become one but it had side effects.

The color of your hair will be change and your body will stop aging or more like age slowly. Aria's hair is originally something like blonde but thanks to hidan irokane her hair turn crimson and her body didn't age more from age of 13.

Hihiirokane (緋々イロカネ Lit. Scarlet Coloured Metal)

1. Only a certain type of personality can awaken Hihiirokane. The succesor has to be passionate and prideful. He/she has to have a personality akin to that of a child.
2. The succesor's heart needs to 'grow'.
3. Before the successor's ability is awoken, they have to coexist with the Hihiirokane for at least 3 years. It cannot leave the successor's body.

And lastly are the bloodlines. The main characters of hidan no aria mostly had a special background or known background. It helps to pass on the skills because in this series. The well known people or researchers can pass down their skills and knowledge for example are Holmes and Lupin.

There's more notable people involved but that's more likely it.

EDIT:

Additional info

Spoiler:

About the Irokane and ability users. There are certain bloodlines that allows to pass on certain skills like Hysteria Mode of the Tohyama bloodline. It's special ability for those specific family but with Irokane and a certain degree of knowledge of the ability it can be learn but it's really hard to do so. To learn the other moves of other choutei one needs to be extremely skilled but it's possible though the chances are probably close to zero.