I think it makes sense to test from the server itself because otherwise I would test network infrastructure. While that is interesting too, I am trying to figure out what the server (VM) can handle first.

I just tried Apache Bench:

ab -n 1000 -c 100 'https://www.mysite.com'

    Concurrency Level:      100
    Time taken for tests:   1.447 seconds
    Complete requests:      1000
    Failed requests:        0
    Requests per second:    691.19 [#/sec] (mean)
    Time per request:       144.679 [ms] (mean)
    Time per request:       1.447 [ms] (mean, across all concurrent requests)

Wow, that is fast. Around 700 requests per second!

Upping it 10x times to 10k requests ...

    Requests per second:    844.99 [#/sec] (mean)

Even faster!