Fractint has many different graphics modes for use with different monitors. You will almost certainly find one that suits you. To change video modes, press delete. This brings up a screen showing a list of possible graphics modes. At the very left of each line it shows the hotkey(s) (if any) for that graphics mode. For instance, Shift-F7 is 1024*768 pixels / 256 colors.

If you are running Fractint under Windows (in a DOS window), you can use the "disk video" options. Disk video modes use your video RAM to store the image (instead of putting it on your monitor). This means you can run it in the background while you do other stuff with your computer. Disk video modes are at the bottom of the list (use "page down" to get there fast).