When using an init system with Linux, you are most likely going to be using Systemd. Systemd is what comes with the majority of Linux distros as of current. However, there has been a lot of criticism against Systemd. Luckily, there are other init systems that you can use. I am going to provide some of the alternatives, and you can decide for yourself what you would like to use as a init system.
There’s also InitWare which is a fork/reimplementation of systemd with less interdependent parts. That means it doesn’t only run on Linux but also BSD and possibly other kernels.