Verdict
Bitcoin is the path of least resistance. Lightning makes it instant.
Almost everyone holding crypto holds some Bitcoin, and almost every wallet can pay on-chain. That makes BTC the easiest way to get a no-KYC server running — and with Lightning, the fastest. The trade-off is privacy: Bitcoin is pseudonymous and writes to a public ledger.
If you want the simplest path, pay in Bitcoin. If you want the payment itself to leave no public trace, pay in Monero instead. Both deploy a server in about ninety seconds, and neither asks your name.