I am very happy with Aldi. I agree that sometimes the produce spoils too quickly and there are some things that my family doesn't care for so I skip those items. What I usually do is shop Aldi first and then go to the my other two grocery stores for loss leaders as well as the balance of what I couldn't get at Aldi. I usually do an Aldi trip one to two times a month.
Here are some of my family's favorites (I have a 6yo DD and 3yo DS):
Cereal, milk, eggs, peanut butter, jelly, ketchup, snack foods, cheeses, frozen juices, diapers, rice, tortillas, chicken breasts, chubs of ground beef, corn dogs, bread, eng muffins, kids yogurts, bagels, cream cheese....that's most of it.
What I did was try one of each item when I started going and if DH said NOPE then I didn't buy it next time. He has some rules - Hellmans Mayo, B&M baked beans, fresh deli lunchmeat - if that's all it takes to make him happy then I stock up on his favorites when on sale. Although a few times I gave him something without telling him to see his reaction - some good - some not.
Enjoy your Aldi shopping - I think if you have one close enough it is worth it.