Woven wraps will do you forever. Others will too but IMO they're less ideal. There are pros and cons to everything, so the goal of owning a bunch is to get all the benefits. LOL!
Mei tais are not name brands, they're a type of carrier that's basically a square with 4 straps coming out of them. There are a ton of brands though each with their own pros adn cons. Overall, IMO, MTs are not great for newborns and I personally don't prefer them until the LO is old enough to go legs out.
Blue Celery is a brand and they're stretchy
afaik so they're useable for a limited amount of time.
Didy is a brand name of woven wrap. (Short for Didymos)