I know some parents and babies find some things necessities, that others don't, but for us here's the list from our experience first time around. Your mileage may vary.

Necessities:
- Cloth dipes
- Good, water soluble detergent for dipes
- Boppy
- Receiving blankets for swaddling
- Lap Pads (they're tightly woven cotton and waterproof-ish and great for putting under baby at diaper changes)
- Nursing pads
- No-wire, stretchy nursing bras
- Hotsling (then mei tai, then Ergo -- at last that was our preference in order of when we used them)
- Papasan style swing (though I'm looking into the Amby Bed for this babe)
- Carseat (we started with an infant seat, and I'm glad as Winnie was small at birth -- 6#6oz and a convertible seat would've been far too big). I washed the cover in cold water and lots of natural fabric softener and Dawn to help remove the flame retardent chems -- hang to dry though as don't want to shrink it
- Baby monitors (our house is big)
- Baby fingernail clippers
- Nasal aspirator
- Socks and hats
- Contoured changing pad that sits on top of dresser
- Small lamp that takes a nightlight bulb for nighttime diaper changes in low light
- SnugTuck bolster pillow for co-sleeping
- Sturdy, non-gadgety high chair for later on (the more gadgets, the more places food can get)
- ETA: Glider/rocking chair (can't believe I forgot that one!)
Not necessary but nice to have:
- Clear shower curtain (so baby can see me when I'm showering

)
- Bouncy seat (not the Johnny Jumpup things but the papasan style seat)
- Breast pump (be sure to buy new if you're looking at electric ones)
- Baby washclothes
- Side-snap t-shirts for wearing before cord stump falls off
- Long gowns with elastic at bottom
- Bibs
- Extra Boppy covers
- Wool puddle pads (or you can be cheap like us and get an old thin blanket from the Army/Navy store and cut to fit. Much cheaper and works just as well)
- Organic crib mattress (but, not so much the crib -- and if I could do it all over again I'd invest in an organic mattress for OUR bed instead, but we had the org. crib one and thankfully she's sleeping on it now. New baby will sleep with us until Guinevere's outgrown the crib mattress)
- Pack-n-play (most people either love or hate them. We love ours and used it often as a changing table when she was little, and a bassinet for naps, then later as a playpen for when I was cooking)
- Stroller
- Noise machine/air purifier (but not the ionic ones -- they suck)
- ETA: Nursing stool
Total waste of cash (for us, again, YMMV):
- Baby tub
- Bumbo seat
- Changing table
- Sleep positioner (our baby hated hated hated it. She far preferred sleeping right next to me)
- Crib (though good for temporary playpen when I needed to iron)
- Nursing clothes for me other than bras. I'm a shift lifter. It's just a lot easier.
- Gliding ottoman (nursing stool is so much better)
That's all I can think of right now. And really, all you absolutely have to have are diapers and some clothes. But the necessities I listed all helped us enormously for a variety of reasons, from birth to far past age one.
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