I am not talking about 7-11’s or Family Mart’s, I am talking mom and pop minimarts. Not only do they have day to day items you may need, some can be quite surprising with what they offer.
When you get settled into where you are living, go out and check the local minimarts. Nearly all have the basics, cooking oil, sardines, eggs, soap, shampoo, evaporated milk, and coffee (and beer). Depending how rural you are, you may be able to walk to many minimarts or may need to ride a scooter to the ones 1-2 kms away, check them out, it is worth it.
I like to use several minimarts for common items, you are helping each of the families. On a clear day, I will ride my scooter for 1 km to get beer, soap, shampoo, even eggs, but they do not have evaporated milk. So at the minimart right across the road, I get milk, evaporated milk, yogurt (used is many recipes I cook), plus sugar, salt, and the common items when it is raining.
I found one minimart, that is almost on par with a 7-11, flour, baking powder, several types of cooking oil, plastic-ware for storage containers, etc. Any items in the minimarts is just a few baht more than what you would pay for in a Tesco, so use the local minimarts and save yourself a trip to town or to a Tesco. The few baht extra would cost you that in petrol, traffic, time, and on the plus side, you are helping the locals, not a corporation.