I haven't used the grocery game though I know a lot of people love it. (I just didn't want to pay for it, to tell the truth, since I can't see how it works firsthand BEFORE paying)...that's just me.
As for the Tom Thumb coupons, I do think you misread it. As a previous poster said, usually with TT coupons, it will say "limit 1 with a an additional $10 purchase". What that means is that you'd buy just one of what the coupon says for that price, but you can't just walk in and get that one thing and walk out. They want you to spend at least $10 in the store (could be anything that you'd be buying anyway). The $10 is just $10, not off any specific price. The "participating items" will usually be the things all lumped together in the sales paper under that heading, or if it's "10 for 10" or whatever, you could mix/match--10 of that 1 thing, or 1 of 10 things with that sign. If it says "2 for 5", you have to read closer: sometimes that means 2 of the same thing for $5 worded something like "when you buy 2", and sometimes it just means the price is $2.50 so you just have to pay some attention. It's really not as confusing as it sounds, you just have to read it.
I'm quite busy too, but still have the time to do some basics to save money. I keep a running "inventory" in my kitchen of basics that are always there. I have a little magnetic notepad I got from Michaels for $1 on my fridge and everyone knows that when something is running very low, write it down for me on that pad, so I'll never run out of the basics. On Thursday we get the sales papers in the mail and I'll take the papers and list what I find from each store that I would want, that would be a good deal (I keep up with prices, so I know when a "sale price" at one store is cheaper everyday at another, etc). Then I decide according to what that week's menu is (and who's got the better deal) which store I'll be shopping at that week. We get the Sunday paper for the coupons and it takes all of 10-15 minutes to go through all the coupons, clip what we would use, and put them in my little coupon file. I think that 10-15 minutes is well worth the savings. I make a weekly menu based on what I have in the house, what's on sale, and the coupons I have.
YESTERDAY I went to Albertsons armed with a plan (from reading the sales papers) and THREE coupons, and bought 8 boneless petite sirloin steaks seasoned in the California garlic medley that we love (advertised buy 1 pack of 4, get 1 pack free), 10 pounds of chicken quarters (advertised 39 cents/pound), a large olive oil with a coupon, a bag of salad with a coupon, a dozen eggs (advertised 99 cents), and a bag of hot dog buns with a coupon, all for $30! The steaks: can be grilled or broiled, we'll have steak and baked potatoes with a veg one day, we can make fajitas with the others in a pack, and the 2nd pack went to the freezer for a future day. The chicken: there's A LOT of it. It can be grilled with my grandpa's special sauce/marinade and served with baked beans and potato salad one day, and I can cook some with lemon pepper in the oven another day. There is plenty to put in a pressure cooker which makes deboning and removing skin ridiculously easy, and even helping me shred it up for casseroles or tortilla soup. A bag of salad isn't the cheapest way to buy produce, but I wanted something fast and easy because I was serving fried fish and shrimp with a little creole rice and needed a quick veg. The hotdog buns can be for hotdogs one day, and buttered with a smidge of garlic powder another day and served as warm garlic bread for a future fettucini dinner. I already have fish in the freezer (that big box of 4lbs of tilapia for LESS than $15 at Walmart equals out to be about $3.72/lb) and we eat a fish meal (or 2) every week. I always have the other stuff in my kitchen anyway, potatoes in the pantry, veggies are in the freezer, pastas, a couple canned beans, and rice a roni are never out of stock, etc. I go to Walmart for the milk, cheese, and stuff to stock my pantry, using coupons and price matching to assist. We eat very well (no hamburger helper, lol) and save a lot of money just eating good food (cut out the sodas and twinky type foods and replace with better options like on-sale pudding cups ($2 at Walmart right now) and celery sticks with Laughing Cow or peanut butter, fruit, stuff like that, and spend an AVERAGE of about $90-110/week (including cleaning supplies and toiletries, though this is less one week and more another week) for a family of 3 with a 2 guests for at least 1 meal/week, sometimes more.I buy meat when on sale, put in the freezer for times it's NOT on sale, and we also eat the leftovers. I may do a rotisserie chicken with potatoes and green beans one day, and another I'll take the leftover chicken, shred it, and make a king ranch casserole that would feed 4-5 people. We could save more money, but I like to have a variety of good food (steak in some form, fish, and chicken every week and ground beef or porkchops once every week or two). It's totally doable, just takes some conscious decision making and some practice. Good luck.
I know this is REALLY long but just wanted to help because my mom didn't know to teach me, and I had to learn from trial and error and tips from mamasource too.