We do not have a limit to the number of visitors. However, there is a physical limit our network can handle.
There is no way to determine the maximum number of visitors your site can sustain. Each site is different and the amount of traffic you can handle will depend on the resources each visitor is using.
Once you are online, you can view your site statistics, like the number of visitors and which browser they use. Your cPanel includes a statistics program called AWStats.
Basically, if you spike the server too hard or for too long, you can be suspended for taking the resources from your fellow shared server users. If you don't want this to happen, you need to move to a dedicated server.
Shared, reseller, and VPS all handle the same amount of traffic. My best recommendation is to upgrade to a dedicated server, or a more powerful dedicated server.