The CrossFit Journal recently posted an article that talk begs the question, which shoe is ideal for CrossFit?  It’s honestly a personal preference.  Because I have wide feet, I have to wear certain shoes, but I will try to wear a pair of them down a lot to become a powerlifting shoe so they will act more flat and level.  A powerlifing shoe allows you to spread your heels apart while pressing into the ground (which is the goal) unlike tennis shoes, which when the heel is pressed out, will roll out as well.  A lot of CrossFitters will wear olympic lifting shoes regardless of the WOD, unless there is a lot of running.  The reason being, they would rather sacrifice a few seconds on the run, then technique and fluidity on the Olympic Lifts.  Makes sense to me. 
Louie Simmons, legendary powerlifting from Westside Barbell, says a cheap and great way to have powerlifting shoes is to get a pair of Chuck Taylors All-Stars (the old school flat tennis shoe).  This being they haven’t changed their style in over 100 years and it effectively allows you to perform your lifts just like a weightlifting shoe, but at a much cheaper price.  When you start looking at your numbers and the difference the shoe makes, then you start realizing what shoe works best for you.  Give them a try, can’t hurt right!?
WOD Level 1:
Lift: 3 x 5 Shoulder Press
WOD:
10 AMRAP
7 KB Swings (1.5pd/1pd)
7 Push-ups