There are various types of carabiners, and here are some examples. There are other types that have screws on the openings and pulleys attached to them, but they aren't used too often in bondage.
(1) Often used in construction. The openings are sharp and capable of cutting rope or fingers, so they aren't recommended for bondage.
(2) This is a decorative carabiner, which should never be used for suspension. It isn't strong enough to support a human body.
Carabiners (3), (4) and (5) can be used for suspension. They're meant for mountain-climbing, so they've undergone strength tests. It's hard to tell from the picture, but they all have a label: KN⇔24. This means that when the opening is closed, they can support an instant weight increase of 24 KN (kilonewtons), or approximately 2.4 tons.
(3) This type is often seen in stores that have mountain climbing goods. Since the bottom has a sharp curve, it's easy for the ropes to get caught on each other.
(4) This oval type carabiner is also often seen with mountain climbing gear. Its curve isn't as sharp as (3)'s, but it's round, so it's still easy for the rope to get overlapped.
Since it's skinny, it can also be difficult to slide the rope through.
(5) I recommend this type of carabiner. It has a wide base that isn't too sloped, and it's just as strong as the others. I found this type at a home supply store.
Also, make sure not to hang too many carabiners on one.
The bottom image is an example of too many carabiners. If you actually tried to do suspension with this many on one carabiner, things would be extremely cramped and hard to manage.
Three should be the maximum number that you ever hang on one.
If you use two different ropes on one carabiner, the ropes could get caught on one another, so you should keep it to one.
In other words, only one rope per carabiner, and only two carabiners per carabiner.
Now then, what should you do if you're working with more than two suspension ropes? Link the carabiners up like a stairway, as shown below.
The biggest problem I see in suspension is the position and order of how carabiners are linked, but I'll leave out that explanation for now.
Also, if you link up a carabiner to a carabiner that already has some rope on it, be sure to push the rope out of the way before you do so.
Please never attach a carabiner overtop some rope.
This won't just make it hard to undo the rope, but could also end up damaging the rope.
Swivels are often used alongside carabiners.
These were originally meant to be used for mountain-climbing to prevent the climbing rope from getting twisted, but in suspension, it's used to spin the bound one in different directions.
Suspension using swivels is slightly more difficult than normal suspension, so I'll explain that in a different section.