I own many mei tais and I have three favorites that I would like to reccomend to you.
www.kozycarrier.com
www.freehandbaby.com
www.babyhawk.com
All three of these come with padded sholder straps although I would imagine you could order one custom made without---I love my padded straps. There is no padding in a mei tai for a babys legs---a very young baby will have his/her legs up inside the carrier and padding is not necessary. I carry my 22 month old in a mei tai and not having padding for the legs has never been an issue.
Congratulations on your upcomming addition and your decission to purchase a mei tai carrier!! Do you already own a sling or pouch for your little one? As mush of a 'mei tai mama' as I am- I personally would reccomend a pouch or ring sling for a babywearing newbie that has no experience with a mei tai. They can be tricky at first- especially with a tiny babe.
Good luck and happy babywearing!
I hope I have answered all your questions- if not feel free to post more!!