A good stretchy wrap is awesome foe a newborn. I prefer the gypsy mama bali baby stretch. It is a hybrid wrap so it is still stretchy and soft for a newborn but it doesn't stretch out as the other stretchy wraps (moby, etc.), so it will last a bit longer. It is lighter too so not as warm to wear.
I also love my open tail RSs. You can adjust them for so many carries and different sized babies - they are super versatile. It is still my go to carrier for quick trips - I just do a hip carry - DD is 22 mos. I love my SBP (sleeping baby productions) RSs - I have a couple of ones that used to be woven wraps and are now RSs. Super supportive and so comfy.
There are some great deals on TBW
and lots of helpful mamas who can help you pick! Have fun shopping!