I have many many slings and I love them all for different reasons. The Moby is a wrap-type sling (actually, a stretchy wrap sling, to be exact) and will work well for a newborn. You might also consider a "Bali Baby Stretch" sling - similar in style to the moby. I have not used a stretch wrap, only a woven wrap which is not as strechy. I LOVE my wrap sling, though!! Tying it is similar to tying your shoes - it takes a little practice, but soon you can do it in no time at all.
I also LOVE my pouch slings. I have 2; a Kangaroo Korner Fleece Pouch and a Slinglings. The KK is stretchy and made of fleece. Very comfy. Very easy. great for newborns. Slingling is also very good - not as stretchy and it took me a little more time to get used to wearing but was much cooler in the summer (my daughter was born June 21 of last year, so you'll be in a similar season).
The thing about ANY sling in the summer is that it's HOT here in Chicago. No matter what you wear, if your baby is right next to you you'll both just be hot. The other thing is that you need to find a good sunscreen or lightweight clothing to cover up your little one because a sling doesn't offer much shade.
I do have a gauze wrap sling (Bali Baby Breeze) that is quite lightweight and good for summer - I used it for both my kids when they were newborn. If you're interested in that one, let me know because I'd actually like to sell it (my kids are too big for it now).
Either way, check reviews at www.thebabywearer.com - it's a great website. And good luck with 2! I didn't think the transition was bad - my kids are 25 months apart.