In the lobby, there are icons next to your gamertag like a fox or a wrench and a bunch of other ones I can't remember. Does anyone know what these mean, if they mean anything at all?

They don't really mean much of anything until you hit legends mode. Levels 10, 20, 30, 40, and 50 are all trophies with laurel wreaths, but the other symbols are random, start at 1s, 4s, and 7s, and with each additional level tack on an extra layer of the symbol (so 12 is a double layer, 13's a triple layer, and 14's a new symbol). Confusing, but again, they don't mean much.
 
If you decide to become a legend once you hit 50 (like prestige in Call of Duty, I guess), that icon changes to a laurel wreath with a roman numeral in it to indicate how many times you've become a legend, from I to X.