I spent a week in hospital before DD, so I can heartily recommend bringing your own pillow. Hospital pillows, unless fresh out of the bag brand new, tend to resemble pancakes in terms of flatness and comfort.
Definitely bring a charger with a loooooonnnngggg cable. Wall plugs in healthcare settings tend to be questionably placed in relation to where they're actually needed. Chargers where you can charge more than one thing are equally valuable.
Snacks. All the snacks. With DD, before labour, I last ate Wednesday at ~5pm. Other than a solitary slice of postnatal toast, I didn't eat again until Friday at 8am. I was ravenous. Fortunately there was an entire box of breakfast bars in my bag, which managed to tide me over until lunch. If you're breastfeeding, keep some snacks to hand, you get hangry.
Big drinks bottle with anti spill lid. If you're breastfeeding, not only do want snacks you'll want a constant supply of drink. Those little piddly plastic cups do nothing if you don't have a second hand to refill them. One big bottle of water/squash to suck on with one hand, while the other hand is busy holding baby to you while it sucks the fluid straight back out of you. Keep it refilled and in reach at all times.
I got my stock of maternity pads via work, so no recommendations other than just go big and unscented. Bulky as all hell, but it did the job. Don't underestimate how many you might need too.
Squeeze bottle to use in the toilet. I used an old sports bottle. I had a second degree tear, and therefore some stitches. Getting pee on them is like jabbing slivers of glass coated in acid into your foof. Gently squirting some warm water over the area while peeing was a game changer.
IMO, don't fanny about with oils. If you want to chill your pads, just slip some in a bag into the freezer and change regularly.