For cross training shoes, I personally have bought three pairs of Nike Metcons, starting with the 2s and now owning a pair of all-black 4s. As someone who does CrossFit 4-5 times a week, I needed something that would hold up to grueling workouts and be comfortable to wear even outside the gym.
I found this all in the Nike Metcon 4, which while on the pricier side ($130 here), I believe you should buy for quality and with the intention of getting years out of a shoe. Structure wise, these shoes are awesome and have spared with many an injury thanks to their flat soles and grip.
Contributor: Andrew Clark, Duckpin