The tan canvas bags with blue handles from Trader Joes are seriously THE BEST!!
They can hold a lot of weight, with no worries about breaking, and are pretty roomie.
You can toss them in the wash, and they clean up perfectly. I think they sell for $5
I’ve been using several of mine for years, and they are still going strong.
They also just got a new super cute seasonal cooler bag - it’s hot pink with a bright yellow interior, for only $8. It feels pretty sturdy, and can hold a lot!
After I bring my groceries in and put them away, I will hang the empty bags on the doorknob so I remember to grab them on my way out and bring them back out to the car the next time I leave.
My state now requires you to bring your own bags, so I’m glad I got into the habit on my own a couple of years ago. They did try to ween folks off slowly - at first they offered super thick reusable plastic bags and then they went to charging for paper bags (most places have phased that out completely now too)… Now you just bring your own or hand carry your stuff.