For a small business, I almost always recommend designing an abstract logo icon based on the problem you're solving for your clients instead of going with a representational logo. 

But, there are usually exceptions to every rule.

Here are two occasions where representational logos (logos that look like something, like a car or a baby or an animal, for example) make more sense than abstract logos:

  • Where the business is selling a physical product, which people are buying because they want to have it. Sometimes the greatest reason that customers buy is because they want to own the thing in question. It might make sense to actually draw your product as your logo in this case. 
  • Where the rest of the logo is mysterious. For example, if you're promoting a service with a long name, and you've chosen to use initials only in the logo. In this case, where the name of the business is not used in full, having a representational logo to clue the viewer in on what the logo is all about can really help to make the logo more accessible instead of adding to the mystery.