Aldi essentials (for me) nappies (if I need to get some emergency disposables), baby wipes, tinned tomatoes, passata, balsamic vinegar, cereals (we eat their 'weetabix', 'shredded wheat', 'bran flakes' and 'cheerios'), tomato puree, olive oil, pasta, tinned sweetcorn and pineapple (all their other fruits seem to be in syrup), tomato ketchup, herbs and spices, flours and baking supplies (sugars, yeast, dried fruits etc, baking powder...), soya milk (if you use it in your family) and cleaning goods (washing up liquid, dishwasher tablets, washing powder, anti-bac spray..). All non-perishable and good quality.
I'd steer clear of their tinned soups and pasta sauces.
Will let you know if I think of anything else.