Understanding agents selecting among markets Let's say an entrepreneur can choose between starting a business in a competitive market with zero economic profit, and starting a business in a market that is not perfectly competitive with positive economic profit. We would perhaps expect in an equilibrium that there would be no competitive markets unless there were no opportunities for economic profit anywhere. Where could I find more information on the structure of markets in this regard?
If a market has free entry, then profit will tend to zero in the long run. Monopolistic competition and perfect competition are both characterized by zero long-run profit. Of course a firm would prefer to enter a market in which long run profits can be earned, but such markets are characterized by barriers to entry. 

To better understand this, consider a market in which firms can enter with entry cost $c$. Then, in long-run equilibrium, the profit that will be earned by incumbent firms cannot exceed $c$, otherwise potential entrants would have an incentive to enter the market.