Cloth Diapers: Obviously, diapers are something you'll need. As a must, you need at least 12 diapers, but it is doubtful you would do laundry every single day, so having 24 diapers is nice. I actually did get by with 7 cloth diapers for two months with a 6 month old baby, so it is doable!
Baby Carrier: With both my babies I don't know what I would do without one! I have tried so many carriers, all of them have pros and cons, you just have to try a couple to see what you like. Some moms love wraps, some love soft structured carriers (like the Boba or Ergo), many (like me) love both for different purposes. To me life without a carrier would be like life without a third hand, and we all wish we had one at one point or another!
Bibs: I consider a bib a necessity. Who has the time to spend on trying to get stains out? I don't. While you could just let the baby try solids while they are naked, most times I can't do that because our house isn't toasty comfy September through April, it can get chilly and I don't want to undress the baby just to save the clothes - so bibs are a must. We've made a habit of wearing them and the kids never complain.
Non-toxic crib mattress: Babies spend so much time in their beds slumbering away, this place simply must be safe for them. There are so many toxins in regular mattresses, it is disturbing. I believe it is a worthwhile investment for the health of your baby, even if it costs twice that of a regular toxic mattress with fire retardants.
Non-toxic teether: We are in the throes of teething, it is a tough battle! A good teether for baby is a must to keep them chewing on something non-toxic while their first teeth come out. While you may find something at home that your child may like gnawing on, you can't be sure what is in the material - so it is important for spend a few bucks on something that you know is not toxic.
Stroller that converts to a double: Okay, so this isn't a must, but oh-so-nice-to-have. If you have one baby, chances are it will not be your last. Strollers that convert to a double just make sense don't you think? I think most strollers should be able to do that, though I wish there were more like it in an affordable price range. the iCandy Peach is an awesome one that will grow with you from holding a newborn in a bassinet, to holding two toddlers!