Yes it is hard to breastfeeding be it latching or pumping, thumb ups for you!
I used to pump at work and these are the list of the things in my pump tote bag:
1. Nursing cover
2. sterilizing tablet & water to soak the pump parts after washed clean with soap & water (pigeon/milton, can get them from baby store/unity pharmacy)
or using Medela quick clean wipes - you will need clean boiled water to rinse
3. clean ziplock plastic / airtight container to keep washed pump parts for next use
4. Breastmilk storage bags / bottles, placed in the cooler bag with ice packs to bring home (keep cool up to 6-8 hours)
For older baby, like my 10 months old, sometimes I just clean the valve in the sink with soap and water, then rinse again with hot water. Or once in a while, if I'm rushed, I stick them in the fridge until I have time to clean them.
It is up to individual but the basic cleanliness must be adapt.
You may want to view other articles on how to store breast milk at this link
Baby and Kids Fashion: Breastmilk storage bag
Hope this can be a good reference for you