Well from personal experience with a small website the biggest things you have to deal with are web crawlers trying to vacuum up every last ounce of data they can find and web crawlers trying to find obvious backdoors like trying default WordPress logins (even if you’re not running WordPress). Make sure your software is properly configured and up to date and you’re safe. Some isolation is still a good idea but don’t lose sleep on which one because they’re all still overkill in this case.
On the other hand if you’re running a service that would be actively targeted by a large government enforcement agency or some other very wealthy and highly motivated entity, then complete physical isolation would be the only acceptable answer but with even more protocols to prevent contamination or identification as there have been attacks demonstrated that could infiltrate even air-gapped environments and that’s assuming you could hide it well enough for them not to just come physically compromise it (without you even knowing).
Keep in mind if you want to use any of these technologies because you want to learn them or just think they’re neat, then please do! I suspect a lot of people with these types of home setups are doing it mostly for that reason and not because it is absolutely necessary for security purposes.
Wait, there are people who don’t realize all the major newspapers are owned by billionaires and thus have severe capital and corporate biases independent of their policial leaning?