Both of those scenarios have problems. Scenario 1 has a ramp-up period of only one second. I can't tell you what the right ramp-up period is, but you can figure it out with experimentation. It almost certainly needs to be greater than one second.
Scenario 2 has 60,000 threads. The right number will depend on your JMeter machine and how JMeter is interacting with the site, but it is almost certainly closer to 500 than 60,000.
Of course, your real question was how to measure whether the site can handle 500 req/sec. You haven't given us enough information to answer the question, so I will make some assumptions:
- Every request is exactly the same, i.e. no authentication, and no request depends on having visited the site before. If that's true, I can forget about users and focus on requests.
- The site runs on exactly one machine, and it has four cores. Your site can't handle more simultaneous requests than the number of cores on the machine(s) that are running it. That means at any moment the site can't actively work on more than 4 simultaneous requests.
Under those assumptions, I would measure with 4 threads, then with 8 threads, then with 16 threads, and so on, until you stop seeing any improvements. (At some point performance will get worse because either your server or your JMeter machine will bog down.)