Do you plan to run something more serious than github, basecamp or shopify? Usually it is not rails, which is the bottleneck, but the architecture of your application.
As a matter of fact, yes. Not as big as GitHub, but bigger than Shopify. So the choice of application server matters, as well as how easy it is to scale and provision that server.
Shopify has 800,000 customers, 4,000+ employees, and handles over $40,000,000,000 per year. And you're building something from scratch, starting today, that is going to be bigger than Shopify in a fast enough timeframe that your Rails server today is the biggest concern?
"Bigger than a shopify website" is a possible interpretation.
Something doesn’t add up: You have have a high profile project that is bigger than Shopify (!) but you ask a question that seems like the first question you should type into google to research this if you were interested.
Any server is fast enough. If your web app is literally doing anything other than rendering empty pages the time a request spends in the web server will be an insignificant fraction of your total response time.
Puma is definitely the fastest or one of the fastest. It's also the default in Rails now. https://github.com/puma/puma
I don't know if it's the fastest, but I've had good success using Puma with Ruby on Rails in a real-world production site. That said, if performance is your goal, then the web server is only a small part of it. In my experience, the way to get a high-performing Ruby on Rails application is primarily through fragment caching and using a CDN. You can get excellent performance with very little effort that way.
You should probably ask Github, they run their main site on Rails.
Wow, got down voted for asking a question on which web application server I should use with Rails today. Really?
Because people are tired of hearing "Rails is so slow". It's been a dead horse for 10 years now, in 2019 it just feels like you're trolling.