Congratulations on your growing family!
Most women I've known -- myself included -- have been really happy to have a breastpump when baby arrived -- we faced either oversupply or undersupply (my issue was the latter) and either way a pump is a useful tool. I did take a used one from a friend, sterilized or replaced the obvious touched-the-milk parts, and didn't sweat the rest.
Other than that, when baby arrives, you need around a week of seasonally appropriate clothes, enough diapers of whatever flavor you want to have handy for about the same length of time (a week's worth), some receiving blankets, some random and scruffy (or not) cloths for wiping up messes, somewhere safe for baby to sleep, almost certainly a carseat, and lots and lots and lots of ready-to-eat (or nearly ready-to-eat) food (for you!).
There's other stuff you do or will need, and no harm in trying to anticipate it, but in my experience you will develop really strong opinions about what those things are and they will not jibe with what you thought before baby arrived. Turns out for example that I have really, really strong opinions about appropriate baby clothes: only onesies, and all short-sleeved onesies should have full snap fronts (so they don't have to be pulled over baby's head) whereas all long-sleeved/legged onesies should have zippers and NO SNAPS because who the heck wants to be trying to line those stupid snaps up after a 2 a.m. diaper change? No one. And at ~2 (?) months I had a desperate need for a battery-powered mobile that could be attached to the crib and that would run uninterrupted for 15 minutes -- as opposed to the lovely, free windup one we had been given that ran for 5 minutes. The battery-powered one meant I could leave a content-yet-awake baby alone in the crib long enough that I could (wait for it) take. a. shower. Magical.
And we had a carseat with a base that also went into a (simple, inexpensive) stroller -- they were Graco products -- and OMG did I love both of those things with all my heart. But other parents will tell you that the carseat-base system is an abomination and that strollers are evil (and for the record I also baby-wore, though I was not a fan of, among other popular options, the Ergo or Beco, which many others swear by, but I STILL loved the stroller AND the lift-out carseat as well as the inexpensive sling carrier I eventually found as something that worked well for me. The Boppy pillow that many had sworn was the Best Thing Ever, in contrast -- eh. I mean, I didn't hate it, but I didn't use it much either).
Long story short, there are a few things you want to have on hand for sure when baby arrives -- see list above, and those others have offered. If you live in the US, are middle- to high-SES, and this is a first baby, there are things people will want to give you (ether as gifts or hand-me-down) and you should let them, trying to provide guidance encouraging them to get you the stuff you think you most need/want, if appropriate. If possible, you should just hang on to everything you are given until baby is 2 or 3 months old and then return (or pass along) the stuff you don't use (if it's infant stuff, obviously, stuff for later stages, save 'til later). If you live in a dense urban area (or elsewhere) in a tiny place, then you may need to be more strategic about what you keep/pass along sooner. And you should anticipate that you'll get some things wrong or otherwise identify stuff you need/want that you didn't anticipate needing/wanting, and when that happens, you should get it (within reason of course). Because the early months really aren't the time to try to tough it out, instead, take gentle care of yourself as well as your little one as you adapt to the many changes s/he brings to your life.
And remember, Amazon (etc.) will ship stuff to your home, you don't, in fact, need to have everything on hand at the beginning -- just the essentials.