If you want high anonymity, I would skip the server all
together. Just use the TOR/ONION network.
Even if you rent a server, it can be traced back you, because
you'll pay with a credit card.
With the TOR/ONION network it's pretty much completely
anonymous. Unless the all the hops(computers you are connecting
through) are working against you and logging the traffic, it's
nearly impossible to tell where the transmission originated.