You can set the new tab page to about:blank if you want to have a blank page.
Current Firefox versions show the URL in the location bar of the new tab page if you set the page via browser.newtab.url.
If you have set the about:home page already then you can middle-click the toolbar home button to open that page in a new tab instead of clicking the plus button on the tab bar (you can move the Home button to the tab bar if you want).

Thanks for the fast answer cor-el!

Actually, I already have everything set up. The new tab shows the page I want, as does the home page. The problem is, I wanted to know if there is a way to open that new tab with the location bar empty, because as I said, on my friend's browser (same page, same config) it opens without anything on it, just like about:home, about:newtab or about:blank (in fact, it shows the default message saying to write an address)

You only see a blank location bar with the built-in about pages AFAIK, but not if you set a real web page.

Note that pressing ESC highlights (select) the full text in the location bar, so pressing ESC before you start typing a new URL should remove the existing entry.

Hi Kregan, when I switch from about:newtab to a real URL, the tab opens with the URL selected, so anything I type would replace it. But as far as having it blank, I'm not aware of any built-in way to do that.

First, thanks both for your answers! I will check with that friend of mine if he knows what happened that could possibly force that behavior. It seems it's not normal nor a special configuration, or anything specific to FF so I'll just mark as solved. Anyway, I appreciate all the efforts! :D

Your friend may still be using an older Firefox version that not yet shows the URL in the location bar like the current release does when a new tab is opened.