You still may have to go to GE for some things ( and they still may not have them ) but you can really get pretty much anything you need at Aldi for a great price.
Eggs are cheap, Giant Frozen Pizzas are cheap, Canned and Fresh veg are cheap, and Bread and Coffee are cheap ( but you can probably save enough money here to go a splurge at a coffee roasters or bakery on these goods).
You can even get a pretty good deal on household items for the kitchen and bath like storage bins, scales, blenders, and electric heaters that look like fireplaces.
AND MOST IMPORTANTLY: Basic spices are ample and cheap.
Just make sure to bring a quarter to rent a shopping cart and your own shopping bags if you do not want to buy any (which I agree with and always forget to do)