I have both the Close baby carrier and the Baby Bjorn. When Thomas first came out of hospital he weighed about 5lb and I used the Close carrier loads. It was fantastic and he loved being in it and would sleep for hours. I also liked the fact that he was tucked right into me so if I went somewhere, people could have a peek at him but he wouldn't get passed around (which I really didn't want as he was so tiny and I didn't want him to catch any germs).
Once he got bigger, I started using the Baby Bjorn sling instead as it was much easier to get him in and out of. I still occasionally use this one (walked to baby group with him in it this morning) but at 13lb 7oz, he is now a bit heavy and my back starts to hurt after a while.
I bought the Close carrier new at the baby show when I was pregnant and got the Baby Bjorn one off ebay. If you can get a second hand one, it may be a good idea as you will probably only use it for a few months. Do any of your friends have one you could try before you get one as I think slings are quite a personal thing and different people may find different ones suit them better.