How do you test a new server provider?

Answers will vary. But there exist one true test of the provider's ability to stick with you through thick and thin: it's the Turing test!

See, providers have regressed (economy of scale and all) to the degree where their responses to inquiries/emails/requests are indiscernible from early wannabe AI chatbot implementations.

Take the time to email/call your potential provider and ask questions regarding the service. Do the responses pass the smell test? Is sales completely clueless and unable to answer questions about simple technical matters (red flag)? Can support carry out requests that aren't scripted?

Trust your instinct and common sense.

I put up an extremely offensive (yet legal) image or video, then link to it from a conservative forum. I then log the date/time and calculate how long, if at all, my server remains online. If it can handle the DoS or DDoS, phase one is good. If the provider doesn't cave to demands to remove the site, then phase two is good. At that point, I would call them a good server provider.

If you are referring to benchmarking, I might do a few quick tests with bonnie++ and openssl speed tests for the server itself and some iperf3 tests for the network throughput.