Having your own instance can be bad for privacy, as all your searches come from your IP (hosted at home) or the same IP (hosted on a server). They might not be traced to you personally, but you might still get personalized results or your search may still be tracked, depending on how they track you.
That's circumvented when using it with some or better many other people. But then, you need to trust the admin of that instance.
Self-hosted is easy if you know a bit about servers. You need a domain pointing to a server. If it's the only thing hosted on that server and you have set up docker on it, you can just follow their instructions here to get it running in less than 5 minutes (assuming you run the default config and don't customize all of the settings for a while): https://github.com/searxng/searxng-docker?tab=readme-ov-file#how-to-use-it