I've used Fiverr many times - it's usually great. The key to success, I think, is "hiring" multiple people. You basically search for "logo design" pick someone that has a few example logos you like, pick their cheapest option that includes a transparent PNG file, and then answer their questions. Then, do it again with another designer. Then you get two different people creating options for you and with this approach, I always end up getting something that I like. You can also ask them to make tweaks. The logo I am using was a couple of small iterations, you should feel free to ask for changes - they want your good review.
They'll ask you questions like: What is the name of your project? Do you have a slogan? What colors do you like? Etc. You can answer some/all of their questions.
It's a useful service.
Here's a link to the guy who made the logo for AA (by the way the bar above the A was his idea!!!): https://www.fiverr.com/graficjungle