I provided a brief comment about each mode, that you will see as you use the slide viewer.
The bottom line, though: No ambient light present, if you want the best, most accurate image, choose Reference. It's also as good a mode to use to start a calibration from.
With ambient light present, or if you have friends and don't want to watch in dark cave mode, without any adjustment Bright Cinema had my preferred picture. I used it for almost all non movie viewing, and for movie viewing with more than a little ambient light in the room.
I liked the Cinema 2 for black and white movies, but I liked better, Epson's implementation which adds a touch of sepia tone to duplicate the way those classics looked, "back in the day."
The interesting thing to note, is that there isn't a single mode that even remotely looks bad, although Game mode can see a little over the top.
Next page is Warranty. Many folks don't give it much weight, but it is one of a projector's most valuable features, IF YOU NEED IT!