The Senshi System

How new warriors are decided
Unlike the hereditary system of Sol's Sailor Senshi, where the daughters of the current Sailor Senshi will inherit the position, the Senshi of Kui-Shen are chosen individually by the semi-conscious "crystal cores" of each planet in the solar system. Thus, it is rare for previous Senshi be directly related to each other.

All candidates who want to become a Sailor Senshi or a Guardian (the male equivalent) go through a highly specialized training/selection process. The skills learned allow those who are not chosen to support the Senshi.

After the Senshi dies or becomes unable to do their duty, the power is returned to the planet's core until a successor is chosen. The delay between old Senshi and successor varies from case to case, so it's not uncommon to have periods of time where there are two Senshi of the same gender, or no female/male Senshi at all.

In general, there's a pretty quick turn-over for Senshi/Guardians.

 

Planet Specific

Ryuza - Warriors of Epsilon
[Female] Join the Priestess Order at one of their hidden compounds. The girls are trained how to be Sailor Epsilon and how to support her if not chosen by the Epsilon Crystal.

[Male] Enter the "Shadows" organization though military promotion or direct invitation by a team's leader. The Epsilon Guardian is selected secretly, without notifying anyone outside of the team he was based in.
 

Rusalki - Warriors of Theta
[Female] Attend a Gathering and participate in various competitions. The champions of certain categories are invited to join the Warrior Order, where they are trained primarily to be Sailor Theta and how to support her powers. The Warrior Order doubles as the world's police.

[Male] Attend a Gathering and participate in various competitions. The champions of certain categories are invited to join the Guardian Order, where they are trained primarily to the Theta Guardian and how to support him. The Guardian Order doubles as an off-world attack force.

 
Shen-hu - Warriors of Vega
[Female] The clans nominate members to participate in a competition where the exceptionally skilled are tattooed with a symbol that marks them as a Sailor Vega candidate. All Shen-hu are already trained from birth to be a Warrior of Vega so they get no additional training, only a position of prestige.

[Male] The clans nominate members to participate in a competition where the exceptionally skilled are tattooed with a symbol that marks them as a Vega Guardian candidate. All Shen-hu are already trained from birth to be a Warrior of Vega so they get no additional training, only a position of prestige.