One thing with Costco, you can bring a buddy on your trip and they can use your card too.
My mom and I go to Costco together. I do the upgraded membership, which yes, is more expensive, it's like $100 in my area, rather than the $50 regular membership. I do this because they give 2% of all that is spent on the card back. I haven't paid for the membership in 2 years because when my mom and I both go, the total of both of our trips is applied and I get enough back to cover the membership. The other thing we do is split/share things, like produce. Often, there's too much for either of us to use up before the item goes bad, but it's still a great deal, like tomatos for $1.29 a lb, but they are sold in like 8 tomato packages. I just can't use 8 toms for my family before they go bad.
For me, chicken I can usually get for $0.89 a lb at Costco, it's usually well over $1 a lb at the store, on sale. Most of the time, meat I can usually break even on-find the same price at Costco as at Walmart, but I also usually find that it's better quality at Costco. My Costco also only sells organic frozen veggies, they don't even sell regular ones. And those usually average $1 a lb or so, and are sold in bulk packages of like 5lbs. Usually with sales and coupons I can get regular frozen veggies at the regular grocery for much less (even free) but for organics, that's a great deal. Milk and eggs are also usually a great deal. I don't buy bottled water, but my mom always gets bottled water there, she finds it's a great deal.
Coupons and sales-check around for coupon blogs that apply to your area, you can probably find one that does lots of the matching up for you. That will save you time. And in the end, LOTS of money. You mentioned wanting to average $200 a week for a family of six....this week, I spent $30, for the week, for my family of 4, plus one coming in September. This includes EVERYTHING-food, produce, pet food/supplies for five animals, tp, toiletries, diapers (for 2 because I am in the process of stocking them up for the new one coming as well), cleaning supplies, etc etc. The reason I spent so little is because a)I didn't NEED much. We were out of tp (which we shouldn't have been, but I miscounted) and out of dishwasher detergent, but that and produce was all we needed. Everything else has been stockpiled at great prices. I have a small supply of most things that lasts me between good sales. And b) stacking coupons-using store coupons, like CVS extra bucks, in combination with regular coupons in the paper. I bought 3 things of contact solution this week....for free. I used extra care bucks at cvs and they had a special that gives you the same amount of ecb's back. I also bought that dishwasher detergent that I needed for free. Used a $2 Meijer coupon and a $0.50 off coupon from the newspaper, which Meijer doubled to $1. So I had $3 worth of coupons, and bought a $3 container of detergent, paid nothing for it. Most of the $30 I spent was actually on produce.