I want to host an OBS stream via Twitch, which only shows a background music and a countdown with possibly animated background.
It should not be streamed a game. What requirements do you need for this? In particular - can one realize that by vServer? 2 cores + 2-4GB Ram?
Of course, it depends on what an animated background this is.
If a video is to be played, for example at 25 FPS, then the CPU / RAM memory may be sufficient for this. For everything I would recommend a graphics chip. Will be difficult otherwise.
Since I assume that you want to set up and view the whole thing in OBS, anyway, more graphics performance would be required anyway, because the production of the live image happens locally.