Kodi TTS currently supports eSpeak and Google TTS engines as well as the mpv player. Below is a brief description of each:

eSpeak TTS engine

eSpeak has its own built-in player so you can get by with only installing eSpeak. However, there are several reasons not to:

eSpeak voice quality is a traditional ‘computer’ voice
Google TTS provides a much higher quality of voice than eSpeak
The built-in player does not support caching, reducing responsiveness and increasing cpu load.
mpv can play eSpeak produced wave files, which would allow for caching

Google TTS engine

Requires an external mp3 player, such as mpv

mpv player

Mpv can play mp3 as well as wav audio. Mpv has several desirable features:

Able to adjust the speed (tempo) without altering the pitch. By altering the speed in the player, a cached recording can be played at different speeds without regenerating the recording.
Able to run in ‘slave-mode’ which allows Kodi TTS addon to control mpv better, making it more responsive and reliable.
Slave mode also lets a single mpv instance play many recordings. Without it, mpv would have to be launched for each recording, and there are many.

Installion on Linux

Installation of mpv and eSpeak is simpler on Linux than Windows since they are generally available in Linux distributions. Simply use the system installer and choose:

eSpeak-NG for eSpeak (eSpeak-NG is newer and has a few more capabilities)
mpv for the mpv player