Turn the shirt inside out before it goes in the machine. Wash it cold with the rest of your cotton, on a gentle cycle, and use a normal amount of detergent. Bleach will fade the print and rough up the collar. Fabric softener is not much better. It leaves a film on the graphic and makes the shirt feel slick instead of soft.
Give the heavier tees some room in the drum. A packed load beats the seams against everything else and is how a new shirt starts to pill at the sides. Hang the tee to dry when you can. If you use the dryer, keep the heat low and take the shirt out while it is still a little damp so the neck does not waffle.
If you iron, do it from the inside. A hot plate straight on the ink can flatten the color. Once it is dry, fold it. A shirt left in a heap picks up hard creases across the graphic, and those are the lines you still see the next time you pull it on for a long afternoon at the stove.