I feel like I have a slight prejudice against getting a show line, especially an American show line because I have heard a lot about health problems like hip dysplasia being more prevalent.
All the different types of GSDs are going to have issues with hip dysplatia and other issues. It's a SUPER common misconception that because of the structure of certain lines they're more prone to hip dysplatia, but the disease is genetic (although it can be influenced by how the dog is raised) and through proper testing, you have much greater chances of getting a sound dog. This applies to every type, not just American Show, which is why finding a breeder that does health testing is paramount. In addition to the different lines, you're going to want to do some research in to the various health issues that plague GSDs (hips, elbows, degenerative mylopathy, mega esophagus, etc) so you can find a breeder that tests for the issues you would prefer testing on, and tracks the occurrence of other issues in their lines and the lines of the sires they choose to minimize chances of problems.
Since you don't have a specific goal in mind that one type would be best suited for, when you're thinking about your future dog, think about how you imagine him or her inside your house on a daily basis, and during whatever activities you might be doing. Is your dog laying around while you get things done, following you around the house, begging you to get up and play ball? Is your dog going for hours on end at one particular task, or will you be out and about for just a little bit and you're done? Are you thinking of doing a lot of "for fun" training (whether it's tricks, helpful tasks, or a sport like agility) or are you thinking you're fine with the bare basics?
When you're thinking about all of these things, you might come to realize that the temperament in one line over another really appeals to you. You can also seek out clubs, sports, shows, etc in your area where you will be exposed to the different lines so you can see how the personalities would mesh with your lifestyle. All of this has the added benefit of helping you out when you do find a breeder. If you're very specific in the dog you are looking for, and you find a breeder with a great track record of producing sound dogs and the ability to match them with the right person, no matter what line you go for, you'll get the perfect dog for you.
Here's a great article on the differences between the lines, if you're interested.

It's written by a working dog breeder, but I think she does a good job of pointing out traits that may have a person lean towards the other lines:
(Types of German Shepherds, by Wildhaus Kennels )
Good luck in your search! Have fun researching!
