I've used wrk and siege, siege is a really easy to use tool, but I'm not sure if you can test DELETE or PUT with siege.
Wrk can use provided lua script to generate requests, so DELETE and PUT won't be a problem. AND wrk is a tool that can overpower NGINX static file server, so I think it's fast enough for general purpose load testing.
I've never used boom or Yandex.tank suggested by @Direvius, basically because wrk is simple enough and fit our needs. But JMeter is too complex for me.
