Bubblesbebe
The soft (stretchy) cloth tying ones are really easy to use as you tie them before you put the baby in, meaning no risk of dropping them or squishing them and you're not worrying about it. You can leave it on all day and pop the baby in and out which is brilliant! Although I got on better with slings with DC1, not sure why DC2 just didn't seem to take to them. These slings are cheap and easy to find, you can even make your own (without sewing) from a length of jersey cotton. The downside of this type is that it doesn't last once the baby is about 9-10 kilos, it gets too heavy and uncomfortable because the stretch in the fabric is too much. You can also only do a front carry with them and they tend to be pretty hot as lots of layers on you. Which come to think of it was probably the issue with DC2. Maybe I'll have another winter/autumn baby to try one out with!
You can also get woven fabric slings, which are similar but not stretchy. These are fantastic because they are so versatile - can use right from newborn up to toddler or even preschooler if you can lift them! I've seen photos where people demonstrate the strength of these things by carrying another adult in one - obviously not for long, but it shows how strong they are. You can do so many different carries with these - back, front, hip. And even turn it into a hammock when you're finished carrying babies. IMO these are the most beautiful as well (hippy vibes, if that's your thing.) The downside of this type is there is a strong learning curve, you have to tie around the baby/toddler which takes practice and confidence, and they are expensive.
The type with buckles can be broken down into two main types - ergonomic and non-ergonomic. Ergonomic carriers have a thick waist belt to transfer the baby's weight to your hips, they will often have a clip to connect the two shoulder straps, like the chest clip on hiking backpacks, and the seat of the carrier is wide, supporting baby's legs from knee to knee. The non-ergonomic ones tend to hang all the baby's weight off your shoulders, which is fine if you're a man and/or the baby is very young, again, under 9-10kg or so, but otherwise it will become uncomfortable very quickly. And some of them especially the generic ones that you find in places like Lidl are extremely poor quality and you never really get a secure carry with them at all.
Ergonomic carriers tend to be made by baby carrier specialists and examples include Ergo, Rose & Rebellion, Boba. Non-ergonomic tend to be made by companies that make lots of baby things like Chicco, Cybex, etc. There's also a company called Baby Bjorn who for years were infamous as the non-ergonomic baby carrier specialist, but they have now brought out some ergonomic carriers as well, so just make sure if you look at baby bjorn to get the newer models, not their classic ones.
Pros of buckle carriers is that they are extremely easy to use and the idea of operating buckles and straps is more familiar to most people than tying long pieces of cloth. They also have a more modern/mainstream kind of look, indeed, you can get an enormous variety of designs, anything from flowery and hippyish to batman themed and everything in between, also of course plain colours like black, navy and grey. (If you're interested in a custom made one, BTW, can I shout out to www.pouchlings.com/custom-made-baby-carriers.html - as a bonus you'd be supporting a small business in corona times :) )
Cons of buckle carriers is that they tend not to be suitable from newborn as you need some degree of head control from the baby to use them, there are "newborn inserts" for some of them, but they don't work particularly well, and aren't as supportive as a cloth type carrier. Buckle carriers by their nature as well aren't as adjustable as cloth carriers - you can of course change them for different people wearing them, but you would have to manually adjust the straps each time. You can generally only do a front carry and a back carry, some claim to offer a hip carry but it's unwieldy. They don't cover a wide range of child ages - you have to buy a carrier sized for baby (2-24 months), toddler (6/9m-4y), or preschooler (2-6+y), because they can't be that adjustable. If you (or DH) are larger or very slim, very tall or very short, you might find that standard ones don't fit your own body correctly, it's worth googling to find the waistband lengths of different carriers.
Then there are the less commonly known types of slings - ring and pouch slings, go over one shoulder, can be used from newborn across the chest (great for breastfeeding) or with a baby who can sit on the hip - I found this again, for some reason great with my first, tricky with my second (perhaps he does not like slings??)
Mei Tais (with various spellings as it's transliterated from different Asian languages) - generally a rectangle of cloth with four long straps which you tie. The versatility of a wrap, without the masses of fabric.
Hybrid slings - things like Caboo, which is a stretchy wrap using rings to support parts of the fabric. You have to look at the individual one to see if it's any good.
The vast majority of people get on best with a stretchy wrap from newborn until about 6-9 months or the baby's first summer, if they were born in any month except March-August. Then move on to an ergonomic buckle carrier.