Hi A.,
My family is the same size as yours, 2 adults and 1 little one (9 mos.). We spend about the same, $600/month on mostly food and a few household items. This comes out to $6.00/day per person, which I think is very reasonable.
We rarely, if ever, eat out. My husband and I both pack lunches to take to work, and I buy food from the vending machine about once a week. These are all factors you have to take into account when looking at your food budget.
For food, I shop at Lund's and the Wedge Co-op. I do buy local and organic foods whenever I can. Many people think these stores are outrageously priced, but I "shop the sales" and buy a lot of items in the bulk section, like beans, oatmeal and rice. I could maybe save 50 cents on hamburger if I went somewhere else and bought factory farm meat that's been driven 1,000 miles to my table, but what kind of "savings" is that?
We don't buy much in the way of household products; most of the money goes to food. I make my own laundry detergent, and I use vinegar for most of my cleaning. My son is in cloth diapers and I use cloth menstrual pads.
If it's imperative that you stick to $600/month, I would say that the fewer times you go to the store each month, the more you will save. The most expensive thing you can do is to be making several trips. I go shopping every 2 weeks, when I get paid. Also, you could start eating more meals without meat, as good meat is very expensive these days.
Another tactic you can use is to keep track of the cost of items as you put them in your cart. Before you check out, look at the total--if it's more than your budget, pick out the items you can do without for now.
Good luck!