Hi Cheese,
There are many good quality brands out there that can fit your needs and provide you with a variety of your customers.
To prevent shrinking you can look at cotton that is pre-shrunk and made with ringspun cotton. Ringspun cotton is processed is processed to reduce shrinking. It will still shrink since it is cotton but it is less prone to shrinking.
The other option is to look at cotton polyester blends which. The blend helps to reduce shrinking as well.
For specific brands, Gildan is by far the more reliable for quality and size/fit. Their SoftStyles like the G640 is a popular choice. Other brands like Bella + Canvas, Next Level Apparel, and Anvil are also great choices. The men's or unisex options usually run true to size like the Next Level 6051 or N6210, the Bella + Canvas 3001C or 3413C, and the Anvil 980 are popular options and all have sizes ranging from XS to 3XL.
Best,
Cailey