I use reusable bags, most of which I've made and used for years but I do have a few of those ones you can buy at the grocery store too. What I like best to use is these plastic crates that my grocery store sells too. The carts fit 5 of them so you can get a huge load but only have to transfer 4 or 5 crates from the cart to the car to the house. It's easy to put them away without unpacking too.

As a pp said I also put the bags/totes right back into the car once I'm done unpacking.