My experience is that a gallon of milk will not last for weeks if it’s Chalav Yisrael.
If it comes home from the store not spoiled, I’m happy. Once it comes home not spoiled, it virtually never lasts longer than a week even if the date says it should last two more weeks or longer. So budget for buying milk every week or even more than once a week if it spoils. A gallon is unlikely to last longer than the week.
Off-brand diapers really depend on the brand. From my experience, Kirkland diapers are just fine, but not cheaper than Luvs when you get them on sale and combine with coupons.
Also, another GREAT way for anyone to save money is to buy in the chain supermarkets on sale, and then use coupons. Especially in NJ where its common for them to double coupons. Just an example, I recently got salad dressing in Shoprite for free, combining a sale with a doubled coupon.