2D VTubing
For 2D VTubing, you have a few options:
2D VTubing Options
Live2D
Live2D is the most popular and widely used option for 2D VTubing. Live2D models are widely supported by tracking applications that run on Linux, such as VTube Studio.
Innochi2D
Innochi2D is an open-source alternative to Live2D. It is still in development and not at a 1.0 release yet, so it may have some bugs or missing features. Innochi2D has separate model creation software from Live2D, so you cannot use Live2D models in Innochi2D or vice versa.
PNG Tuber
PNG Tubers use a single or image, or a handful of edited version of an image, with a program to warp, move, and transform the image in response to audio. This option is the easiest to make and set up but has the most limitations.
Live2D & VTube Studio
VTube Studio by denchi is the most popular Live2D tracking application. It supports webcam and iPhone face tracking, as well as audio lip-syncing. VTube Studio is a Windows application, but it runs well on Linux using Proton (see the Running Windows Software on Linux more information).
Installation is straightforward. After setting up Steam and Proton, you can install VTube Studio from Steam. After installation, you need to copy this file to streaming assets folder. You can now use VTube Studio on Linux with some restrictions.
If you have problems launching VTube Studio, try forcing usage of Proton 9.0-4 from Compatibility settings in Steam (right click VTube Studio in your library, go to Properties -> Compatibility): 
WARNING
Apple devices over USB do not work. You can use Apple devices over WiFi or a webcam for face tracking.
WARNING
Sometimes, you might get errors during installation. If this happens, continue, there is decent chance it will still work.
TIP
The file is directly from DenchiSoft, the developer of VTube Studio. It allows VTube Studio to listen for connection from external tracking software, such as VSeeFace.