First off, Phoenix magazine claims they have the best cheese selection- this is NOT true. AT ALL. Their cheese selection is very, very small. A step up from a regular grocery store, but they practically nothing. If you're looking for cheese, go to Whole Foods- they have a HUGE selection of cheese, and a very knowledgable staff- and you can even try any of the selections, which you can't at AJ's.
That said, AJ's is wondrful for other stuff. Wine. Their wine selection is great, and their wine stewards are very helpful. They also have a great, huge selection of cigars. Their meats are great, produce completely overpriced, and already-prepared foods are a great alternative to eating fast food! The breads and pastries are fabulous. Leave everything else to buying at the regular grocery store, like soap and toothpaste.