First of all, it is best to wash your tees inside-out. It may be obvious but it is definitely one of the most important tips on the list. You can also use the zippy-bags for the delicate materials. This helps in preserving the ink on the fabric as well as protects the fabric itself from rubbing against other clothes while washing.
As to the washing machine settings, it is advised to go for cold water temperature and gentle cycle. Use mild laundry detergent and never use bleach. If you want to be 100% sure that your shirts will not be damaged after the washing cycle, separate whites and colored shirts as well.
Do not put your t-shirts in the drier, let them dry naturally (air-dry only). The heat from the drier accelerates the deterioration of the ink and the clothes can act unpredictably when being put in the machine.