I’ve been buying Lansinoh nursing pads from the beginning, and they give you a few storage bags with each box. I think it’s probably only enough for the occasional pumper. Otherwise, the Medela Storage bottles (something like $15 for 15) are also probably a pretty good way to go for the continuous pumper (except you have to wash them). I’ve seen them for cheap on eBay. (all BPA free)
I also found that spending a bit more on the Lansinoh bags which have two layers of zip top well worth it. I cheaped out and tried a less expensive brand and ending up “crying” over the spilled milk that leaked out into the freezer. The smaller Medela bottles are somewhat handy as they screw right onto the pump horns.
After starting with the Gerber brand bags and buying a slightly more expensive box of the Lansinoh bags b/c my local store was out of the Gerber, my son’s babysitter and my husband (the two most likely to know) have asked that I not purchase the Gerber ones anymore. They find the L-bags slightly thicker, less likely to leak, the zippers better, and less likely to puncture if it doesn’t freeze straight (ran into this issue with Gerbers). We’re lucky that we have a small chest freezer that is dedicated to Momma Milk so its more a matter of which shelf to grab from.
That’s what we did! I had a special place that I had reserved for “fresh” milk bags. Once they were frozen flat, I stacked them up in a container-file type system. It made it very easy to know which milk to use first!