There are several services giving a possibility to test ping time to a server. But if I don't have any server on tested hosting yet - how do I test the ping to it? Can I ping hosting web-site it self?
One of the best ways is to do a reverse DNS of the hosting company, once you have found that information, you have to find other sites that share the same IP. You can check that, for instance on reverse IP domain check.
If the server has more than one IP assigned, then you should check all of them.
Browser a few sites from those IPs, that way you can get a real feeling about the response time of the server. If one site is specially slow, discard that one, most probably has internal problems, but if many are slow, then the server is to blame. If you want to be thorough , do the test on a private tab on your browser, on different days and hours.
If you know how to program, you can make a script that uses cURL, without reusing session/connection.
Of course, is the site allows you to host for a few days without charge, do that and compare your loading time with the rest of the sites sharing the same IP as you. Just pay attention to the IP, some hosting companies use to host trial sites on servers with low load and once you hire the service, you get moved to a heavy loaded server. I don't know if that is still a common thing now.
If you can get information from the server, then get as much as you can, use simple tools like phpinfo and similar.
I can advise you look for a hosting with a test/trial period. It can be up to 1 month (you don't need more than that) - that should be enough to test everything.