I have found the connecta carrier about THE easiest to use sling with a newborn. I have 3 at the moment - a velvet one, a printed one (calaveras fabric!) and a solarweave one. (I think they have the solarweave connectas on sale at their home website at the moment too!).
I will attempt to show my pictures of Alfie in the solarweave one (aged 2 weeks). It was very easy to bf in this one as you could swivel it around to position him directly infront of your boob - and then gently lengthen the straps so he was at just the right height to latch on - and the hood made for very discreet coverage! Infact the hood was also great for keeping the sun off his baldy little head when a hat would not fit well!).
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Well, I hope those links to pictures work okay! if not try copying and pasting them into your browser - hopefully that would work
I used the optional chest belt supplied to cinch in the lower part of the carrier to make it fit the width from one knee to the other between his legs. I fastened the waist band of the carrier higher than usual to make a a nice seat for him to sit in - and that way I didn't need to roll up the bottom of the carrier.
The solarweave carrier being made of especially fine material is nice to use with a newborn, and like I said, the hood is handy too - it also has the advantage of being cool, and very quick to dry if you need to wash it. It packs up really small so you can have it in your changebag if you have chosen to go out with the buggy - and just pull it out for cranky moments or bfeeding.
I believe you can use this one in water too - so you could shower in it (put the hood up and be wary of getting soap suds in baby's eyes - infact remember to wash with something babyfriendly!). You could also use it with a bigger baby when going swimming - just for standing around in while minding older kids really, or for wading into the pool and just getting baby used to the environment while feeling secure... you couldn't actually swim while the baby was in it though - that would be silly!
Anyway, all connecta's are great with the newborn (and right up to 4y olds too!), but I found the solarweave one especially versatile and useful.