Automated Install

Is there a solution to automate the installation on Windows PCs?
A command line?
a solution using ansible perhaps?

I am unsure what you want to achieve. You posted this in the server category but tagged TS3.
Let’s break it down:

TeamSpeak Server

The server is distributed as a simple zip file, with no installation required. You can simply download and extract it from a cmd/PS script.

TeamSpeak 3 Client

The TS3 client is distributed as a EXE installer. Those installers are a bit tricky to get running in an unattended way, but it is possible. You can e.g. wrap the installer using exemsi or similar software and install the resulting MSI file through GPOs.

TeamSpeak 5 Client

The TS5 client is distributed as a MSI installer. You can simply install it via GPOs.

I hope this somewhat answers your question.