If what you want to know is response time of the site for a first request, or sever response for starting the handshake, ping is most than enough since that is independent from the content retrieved, the handshake or the headers. It only depends on ICMP requests being allowed.
If you need to calculate loading time, that is different, the best way to do that, and considering that you mention that the page/site is personalized, is to create a page with the same amount and kind of content, create specific no cache rules on your
.htaccess and the use whichever tool you want to test response and loading time.
Of course that page has to do the same work that the normal application does, just with non sensitive data, for that, you should create some fake data on the DB id the is any associated, then the page has to be generated with the same server side technology if you are using any for the normal pages and it has to fetch and load the same images.
Of course that is if you want accurate data. If you don't want to do that work, or you don't need data as accurate as the one you will get with that procedure, then you can use tools like
ab command from Apache or any other simulation tool.