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My pump came with a storage bag and cooler, so I used that. (Also have a Medela). I bought an extra set of pump parts and flanges, Lansinoh storage bags, two hands-free bras, sterilizing wipes (used in the beginning to cut down on my time, but then I would just store all my pump parts in the fridge).

@MrsH: I have the same pump! I eventually bought one extra set of parts, next time I'd buy a third just because there have been some crazy busy weeks where it would've been nice to let some of the parts washing slide .... I'd also recommend buying even more of those little white membrane thingies. That's what I used up the quickest.
I have the little cube that came with my pump bag that holds the ice pack and four bottles. I have nine bottles total, but next time I would buy at least one more set (same as above, would be nice to not stress about washing and drying on super busy days).
I had sterilizing bags and haven't used them much. Have used tons of the bags for freezing my milk though. I never used sterilizing wipes, just paper towels. I have a mini fridge at my desk.
My pump came with the battery pack and I actually HAVE found it useful once! I had to pump at a work retreat and they provided a room for me, but the electrical outlet was too close to a window! So I sat on the floor and used my battery pack.
I have a simple wishes hands free bra - wish I had two of those!

Not much, the only pumping accessories I've needed was milk storage bags and extra bottles:)

Extra parts, a 12 pack of 2.5 oz bottles to pump into (2 oz per side was usually my max per session & I used them instead of bags most of the time), & the car adaptor. Once my son stopped nursing so frequently it was a game-changer to pump in the car during my commute!

I used the battery pack once or twice in a pinch, but not often - it takes 8 batteries and they wear out fast!! My PISA came with a battery pack & cooler bag/ice pack.

Hands free bra and storage bags! I got by with the bare minimum of parts/bottles, but if I had more I could have dishwashed them sometimes instead of hand washing everything every night.

I agree with previous posters. I have found my battery pack useful on occasion. My favorite "nice to have" that I haven't seen listed is an extra power cord. I keep one plugged in at work and one plugged in behind my couch at home. It's one less thing to unpack and pack 4x a day.

Nothing. I have some extra bottles and sterilizing bags that I got in a gift pack. The bottles are good, but I never use the sterilizing bags (I just do the dishwasher).

Target BM bags are my favorite!