How do I pick the best fillet mignon at the supermarket? What should I look for when I'm at the store picking out fillet mignon?  How can I tell by look which pieces are more likely to be higher quality pieces of meat?
Marbling
From my experience working in butcher shops, you want to first look for good marbling (unless you are on a low fat diet). To illustrate:

I prefer personally anywhere between No. 5 and No. 8. No. 9 and up I find a bit excessive, though some people like it that way. I have had some below No. 5 and they were still good, though.
Dry-aging
From Wikipedia article:

The process changes beef by two means. Firstly, moisture is evaporated from the muscle. This creates a greater concentration of beef flavor and taste. Secondly, the beef’s natural enzymes break down the connective tissue in the muscle, which leads to more tender beef.

Some higher-end butcher shops will dry-age their own beef (at considerable expense) but if you don't have a shop nearby that does that, you can also dry-age it yourself.
Other things
I would recommend not to marinate fillet mignon and season it only lightly. If you plan on wrapping it in bacon, as many do, if you wrap it a day or even a few hours ahead of time the meat will absorb more of the smokiness of the bacon.