Most startups' and indie hackers' web apps can run on DigitalOcean's $6 VPS. You can test the market and gauge demand for your app on that VPS.
Nginx is a web server that will handle incoming requests and forwared them to your PHP application. PHP-FPM is a process manager for PHP, it starts a number of processes to handle incoming requests from Nginx.
If we assume that the average request processing time is 100 milliseconds, your server will be able to handle 50 requests per second.