I like a stretchy wrap for a newborn. Moby/Boba/make your own. You can prewrap what's called a "front wrap cross carry" and pop baby in and out as needed without untying. (It's also pretty good for nursing in if you intend to.)
After they're about 3 months old, a stretchy wrap won't really cut it anymore. They're useless after about 15 lbs. (This is why I always recommend getting a used stretchy. They cost a lot less and they aren't used that long.) I used a Mei Tai for my daughter that I bought for about $20 on Ebay.
When she hit 9/10 months old and I wanted to do more back carries, I went for a "soft structured carrier" or SSC. I personally have a Lillebaby. Lillebaby claims they can go from newborn to 35 lbs or so, but I'm not comfy with a newborn. I'm just weird. But a good SSC will allow you to front carry, hip carry, and back carry. I got my Lillebaby off Zulilly for $70 or so, but a good SSC will generally run you $100 or so.
Another great option that works from newborn to toddler is a plain wrap. They are generally woven linens that can be tied in a multitude of ways from newborn to toddler age. They allow for front, hip, and back carries too. You can get relatively inexpensive ones (Little Frog tends to be an inexpensive yet quality one) all the way up to several hundred dollars for some of the more brand names. But a wrap is a very versatile way to carry baby.
Avoid things like Infantino and Bjorn. They're called "crotch danglers" and can be dangerous for a baby's hips if your baby is prone to hip dysplagia. It's generally not a good idea to face baby outward. It's awkward for your back, baby's back, and baby can get overwhelmed quickly. If baby wants to look out, a hip carry is usually best.
If you want to hip carry, you can get a ring sling. These go over one shoulder and under baby butt/hips. They're great for toddlers that want up/down/up/down/up/down and drive you bonkers if you have to reclip/retye/whatever.
That said, babywearing can easily be like cloth diapering. There are bargain and budget options that work very well in almost all cases (be careful on SSC's, the buckles on cheap options can be bad) but you can also find yourself spending hundreds of dollars on beautiful wraps and SSC's. Depends on what you want.
So, for me, I went stretchy to Mei Tai, to SSC. We still use our SSC for things like hiking and she's a 28lb 2 year old. Totally worth it, IMO.