While you may want to get every possible deal, especially when first starting out. However, it's best not to drive to a store that's fairly far away just for one or two deals, unless of course they are deals on items that costs hundreds of dollars or more. If you are going to travel further than the distance of your closest store or stores then try to go to other stores while you are out.
If you have a smartphone then check out the ibotta mobile app and sign up for it. There are numerous apps out there but ibotta is because it’s a great way to get cash back when you purchase select items.
In addition to checking out each store's circular another great way to know about various deals is to follow deal blogs. Couponing in PA is my coupon oriented deal blog, but there are also many others that may strike your fancy.
Before you start couponing do your best to know what the coupon policy is for any store that you frequent. For example some stores will double coupons and others won't. Then there are stores that while they double coupons they will only double one like coupon per day, while others will double four. Many of stores allow for a store coupon to be stacked with a manufacturer coupon. Other situation is that many coupons no longer accept printed coupons with the word free in them. So as you see there can be many variations between store's coupon policies and the better you know the policy the better deals you can gather.
One more tip is to plan your meals - not specifically for the week ahead, but for things you plan on making eventually. Of course you can only do so much with perishable items, but for anything with a longer shelf life you can plan further in advance. For example, if you like to make something that required a specific type of pasta & you see it go on sale or have a coupon for it then buy it, even if it's not on your list of upcoming recipes. This way you can potentially reduce the cost of each recipe that you make since you won't be buying as many ingredients at full price when you ready to make each thing.