From international experience, a winning strategy is that you test aggressively everyone who is symptomatic, as well as carry out a random surveillance of key populations. That's so you know the prevalence of the disease, but more importantly, so you can follow that up by isolating the people who are positive and tracing their contacts. It's a chain that starts with testing but ends with isolation and contact tracing.
I can't give you, off the top of my head, the exact number that will be required, but it would definitely include everyone who is symptomatic, as well as a well-designed surveillance program.