Hi c.herself, where does this site show up? For example:

• Only at startup the first time you use your Firefox shortcut
• "Home" page in a new window (Ctrl+n) or when you click the house icon on the toolbar
• "New tab" page when you click the "+" icon on the tab bar or press Ctrl+t
• Other times/places?

I'll jump ahead with two things:

(1) To check/reset your home page, see: How to set the home page.

(2) To check whether your Firefox shortcut/icon has been hijacked:

The Firefox icon can be set up to launch specific pages at startup (or more specifically, when you use the icon). To check whether that is set:

First, open the shortcut as follows:

• Desktop shortcut: right-click the icon, choose Properties
• Pinned taskbar icon: right-click the icon, right-click Mozilla Firefox, choose Properties

Windows normally will select the Shortcut tab. If not, go ahead and click the Shortcut tab.

You'll see the Target highlighted. On Windows, that usually is no more and no less than the following (depending on 32-bit/64-bit):

"C:\Program Files (x86)\Mozilla Firefox\firefox.exe"
"C:\Program Files\Mozilla Firefox\firefox.exe"

If anything follows after that, try clearing it out.

After OK'ing the Properties dialog, you can test right away to confirm that Firefox now launches only your home page. Either:

• double-click desktop shortcut
• right-click pinned taskbar icon, click Mozilla Firefox

Success?

Just in case the above doesn't do the trick : MapBeast is a browser hijacker .....

Go to the 3-bar menu (or 'Tools') => Addons => Extensions and look for any unfamiliar or suspicious looking extensions.

When you find any : remove them.

Do the same in your system's Control Panel.

However : most malware will be 'hiding' somewhere , so let's run malware scans :

Further information can be found in this article : https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed malware scanners. They all work differently - what one program doesn't pick up, the other might.

Also see (you'll have to scroll all the way down) : http://www.besttechtips.org/how-to-remove-mapbeast-toolbar/