My personal vote for "can do everything carrier from newborn to toddler (to preschooler)" is a wrap, hands down, all the way.
Liam's Mum: since you are leaning toward mei tai, I must say that I find Mei Tai's to be pretty much as comfortable as wraps, similarly easy to use in back and front carries (not very convenient for hip carries, but I don't know why anyone needs a hip carry when they can do a back carry), and I could nurse in it easily and discretely. I'm very small chested and I think the discrete part might not work for a bustier mama.
I think that if you are drawn towards a Mei Tai, that you are more likely to find it easy and intuitive to use, and to like the look of it and WANT to use it, so it will work better all around.
A Mei Tai is cooler than a wrap, in my experience. Though EllaRoo wraps are pretty airy and equally comfortable (IME) to my Didymos Indio.
I think you should buy a Mei Tai and if it fails to fill any of your needs you can sell it or trade it and get a carrier that fills those needs.
The benefits of a wrap that you will miss out on are:
fully encloses a newborn like a cradle or the womb--more cuddly
provides great, versatile head support for infant or sleeping kid (some MTs may also)
good for hip carries, as well as front, or back
if needed it can be a blanket, changing pad, handkerchief or napkin, leash, belt, seatbelt (in a highchair or shopping cart, NOT a car), towel, sunscreen, etc
nursing cover, sun cover, post-preg tummy cover, etc
more versatile so better chance that you will be able to nurse in it