God gave you hands and eyes and a sense of smell. Use them when choosing produce! This is by no means exhaustive but are simple, basic tips to keep in mind as you shop.
Onions, potatoes and root vegetables (turnips, carrots, sweet potatoes....the fruit grows in the ROOTS or underground) should be firm and no weakening or weepy/wet spots, which shows age and/or deterioration. When choosing onions I prefer to buy the sweet variety as they cause very little or no stinging to the eyes when cut!
One of my favorite fresh vegetables is celery. Before grabbing the closest one, check for color and texture. IF THE STALK BENDS DON'T BUY IT. Fresh celery is rigid and has no give. When I get it home I cut off the very end where the stalks are all joined before washing each stalk thoroughly. Then I cut each stalk at the "knuckle", where it branches and the leaves have started to grow. Take a moment to cut a itty bit of the end off the stock that is dead from harvesting. Set this part aside (Don't throw it away!). Cut the majority of the GREEN outer stalks according your preferential length to eat and enjoy. I put mine in a ziplock bag with a tiny bit of water in the bottom to keep them fresh. Some people prefer aluminum foil. For the celery hearts (the inside that is light green or yellow) and the knuckles you removed....Chop finely to your preference a seal in a small ziplock bag before tossing into your freezer. This is great to use when you make vegetable or bean soup for flavor, color and texture!
When buying lettuce, or other fruits and vegetables, don't buy the prepared and packaged kind unless you are super short on time AND plan to use it in short order. In the original package that God created is always best. The more hands that touch it to process it, the closer it is to the end of its shelf life is my experience. For instance, I used to buy bagged salad and end up throwing half or more away because it went bad before I used it. Now I buy fresh lettuce---romaine or other leaf lettuce, never iceberg (very little nutritional value and no flavor!) and it keeps for WEEKS in my refrigerator. The icing on the cake? It is a FRACTION of the price and much fresher. Wash only what you will use and put the rest back in your produce compartment in the fridge. If you must prepare a large quantity with the potential of leftovers, tear the lettuce with your hands vs. cutting with a knife. It bruises the lettuce and the edges turn brown quickly after interaction as a result of contact with the knife.
Making a fruit salad? Add the juice of the fruit you're using, especially pineapple! Don't add apples or bananas until the very last minute because of their short life after being cut. If you must cut ahead of time, squeeze a little citrus juice (or cartoned orange juice) over them to prevent the browning.
Another "problem child" in the browning department is avocado. Who doesn't love guacamole for delicious Mexican food or some sliced on a sandwich? Don't throw out the left overs just because it turns after a tiny bit of time in your fridge. Put in the smallest container it will fit in and then gently press plastic wrap over it to remove most/all of the air. Even if a tiny bit turns brown, the flavor is still good!