There were two problems I had with my own "handmade" bags: 1. they would not stand up and open for me or the cashier to put groceries in them. Kept flopping over. When I tried re-inforcing them to be more sturdy, the weight became a problem. and #2 the first ones I made the handles were too short: an easy fix by making the handles long enough to fit over the shoulder, made much easier to carry multiple bags. I basically solved both problems by just buying the heavier plastic type ones the grocery store sells, usually about 99 cents. They last a long time and if you put your meats in a regular plastic bag, they stay pretty clean.
I would suggest making only one or two to try out before you make a stack of them, that way you can see if they will work for you and if you need to make any adjustments before you have spent a lot of time and effort in making a bunch them.
Every grocery store has its own unique bagging system, some more "friendly" to the "green way" of bagging than others.