Definitely get a stretchy wrap for when they are tiny. You can actually just make one from a length (about 5 metres) of jersey cotton - I know nothing about fabrics, sewing etc and I just went into a fabric shop and asked them to show me the jersey cotton. I went for 100% cotton (some of the commercial makes have lycra etc added which makes them stretchier but less supportive for larger babies) and chose a pattern I liked. It feels like t-shirt material.
You just buy 5 metres of this, and it comes at 60 inches wide, a perfect width for a sling is 20 inches, so you can get three out of this, or do what I did which was to have one 20" wide and one 40" wide. I then just folded the 40" one to 20" before I used it (using the thinner one when small and the thicker one when older) - the best part is, it won't fray at all so absolutely no need to sew! I had to taper the ends down of the wider sling to be able to tie it and it didn't fray even though it was a diagonal cut.
Most of the commercial stretchy wraps (moby, kari me etc) state a weight limit of about 33lbs or 13kg on their websites - I would say that mine became uncomfortable a while before that, my DS is 15 months and 24lb now and I could definitely not carry him in one! The wilkinet website which is a carrier to use on the front and back recommends switching to back carries at about 18-20lbs, which I would say is a good idea of when a stretchy wrap will no longer be supportive enough.
I now use a toddler patapum and find it brilliant - the thing with a toddler is that they are so heavy you really need a carrier to be adjusted correctly, and I found this out today, I had adjusted it to take coats into account and had made it too loose, and he was really heavy and hurting my back. On the way home I made it shorter again and really noticed the difference, even though DS was asleep and was a dead weight.
I wanted to get a woven wrap initially as these are supportive like the stretchy wraps, but more so, and you can use them from birth until age 4 or so, but unfortunately I never got the hang of tying it and tightening it with DS in place, so I found the stretchy wrap which you pre-tie and the soft structured carrier which you pre-adjust the best things for me.