If baby gets most of its nourishment from the breast, with only occasional expressed milk, the type of storage container is not a major consideration. It is only a consideration when most of baby's nourishment is expressed.
Research is conflicting as to which container is best for fresh, unfrozen milk. This is due to leukocyte survival - which one promotes, which destroys or which causes sticking to the side of the container? As a result, some of the latest research suggests glass as the preferred choice.
Milk storage bags are used by many moms. Care needs to be taken that these bags don't leak, causing potential contamination. In one study, a 60% decrease in antibodies and a loss of fat to the sides of the bag were found in the thinner plastic disposable bottle liners. For freezing milk, the thicker pre-sterilized bags designed specifically for breastmilk are preferred. If the thinner bags are used, be sure mom uses two bags, squeezes air out, leaves 1” at top for expansion, closes and seals it, and places it upright in a heavy, plastic container with a lid.
Using glass for freezing is preferred since it is less porous. The second choice is clear, hard plastic (polycarbonate) and the third choice is cloudy, hard plastic (polypropylene). For maximum protection, seal with a solid, single-piece cap.
And of course, instruct mom to clean any hard-sided container with hot, soapy water, rinse well, and allow to dry before using.