They all have pros and cons and it really depends on your personal preferences. I would advise you to see if there is a babywearing group in your area- check meetup.com and yahoo groups. They get together and you can actually try out other mama's slings and carriers to get a feel for them, at least that is how ours worked. And you can sometimes get good deals on used through those moms.
Personally, I hated the Bjorn- so uncomfortable, couldn't carry him for very long without my shoulders being on fire, and they are not good for baby's hips to be in them for long. Ergo is similar but baby doesn't hang from his crotch and the construction is much better for comfort. Downside to the Ergo- kinda bulky to me.
I haven't tried the others but have worn a mei tei briefly and it was more comfortable than Bjorn and not as bulky as an Ergo. I didn't use it when baby weighed much so can't comment on that part. I had a moby wrap and loved it for comfort also, but my son didn't like it after he got heavier. It is great for newborns and infants. Downside to the moby- it is time consuming to put on and bulky. Better for wearing around the house than out and about in the heat. I also had a hotsling (pouch style). Loved it when he was littler, got uncomfortable when he weighed about 15 lbs. (I think, I can't remember.). Super easy to use, great for quick errands in stores, great for using at home when baby is just too clingy and doesn't want to be set down. Downside- only one shoulder supports baby's weight, not both, so it gets uncomfortable a lot faster than a 2 shoulder carrier. Not truly "hands-free" because the one shoulder is a little bit immobilized, but not completely.
I think that sums up my opinions on those, I'm trying to be as brief as possible. As for the safety aspect, I read this article a long time ago when looking at slings, and I was so glad to see the bag slings get recalled. It explains the difference between the recalled type and a hotsling/peanut shell pouch type pretty well. The reason for the recall was that baby's head gets forced down toward their chest in the bag sling, cutting off their airway and they suffocate. The fabric does play a role, but it is more about the positioning. A pouch sling positions baby differently. It doesn't take but a minute for baby to suffocate in that position, so it is unrealistic to think that you would notice something was wrong if baby was asleep (which is a great benefit to using slings- they sleep) and not being vocal or moving around. Personally, I will still use my slings with my next baby, as far as the information goes right now that is out there. I will check again before I use one since that is likely to be a few years. But what I have read currently makes me feel they are ok. The top link is the article, the bottom is a great resource for info on babywearing in general.
http://www.babyslingsafety.blogspot.com/
http://www.thebabywearer.com/
Hope all that helped! Good luck :)