Running the site itself shouldn’t be an issue (any linux capable hardware can run a site) it’s the network side of things that can be more challenging/costly.
Most data centres have things like power generators in case of failure, multiple redundancy connections to the internet in case one goes down, protection from things like DDOS, etc.
Nevertheless if you still want to do it (and as professionally as possible) then…
Good luck and let us know how you get on! 
