Carabiners
Carabiners are a crucial part of your self-suspension kit. I recommend having at least 3, perhaps 5 or more. Carabiners are used to keep your uplines separated and organized, and to build pulleys for lifting. Using a carabiner rather than simply going through your rope bite or hanger and using that as a pulley decreases friction (allowing you to pull up more weight more easily) and is also safer, as rope-on-rope friction can wear down your rope and even cause rope breaks.
Carabiners also provide a “quick release” – there are many situations where unclipping a carabiner is faster than untying, and even faster than cutting rope. This can be a useful safety measure, especially when it allows you to quickly detach non-critical lines. However, in most cases it is safer to lower yourself to the ground slowly than to unclip (or cut) a critical line.
There are many factors to consider when picking carabiners. Always use climbing rated carabiners, never carabiners from a hardware store. Climbing carabiners will always list their ratings on the spine, so they’re fairly easy to identify. Ratings are listed for both gate closed (much stronger) and gate open (much weaker). If a carabiner doesn't have this info on the spine, it is not appropriate to use for suspension.
Shape
Carabiners come in a number of different shapes – ovals, D-shaped, and pear-shaped – and there are variations within these shapes, as well. For hanging your ring from a hard point or attaching your ring to a spinner, you ideally want a D-shaped carabiner (although an oval or pear shaped one will work fine). This is because carabiners are strongest along the spine, so you want to arrange them so most of the weight is oriented there. When you’re attaching a spinner or cargo strap to a pear shaped carabiner, it doesn’t load as directly on the spine as it would in a D-shaped carabiner, and it can also allow some back-and-forth movement that can feel insecure and alarming (as well as making unfortunate clicking sounds).
For pretty much everything other than attaching rings/spinners to each other or a hard point, pear shaped carabiners are optimal. You want to look for a roomy pear shape without a steep “slope” – a more rounded and gradual curve gives you space to form a pulley, and won’t cause your rope to overlap on or under itself and jam. You also want to check that it has a gently curved “lip” (the surface on the inside, where your rope will be rubbing) – some smaller carabiners have quite a small lip, and this can cause additional strain on your rope.
You want to look for carabiners that don’t have a “tooth” on the gate, as this will catch on your rope. Most new models of carabiners are toothless, but it’s something to check. You want large sized carabiners, and this can be impossible to tell if you’re buying online (unfortunately, they don’t seem to list sizes). The more room you have on the inside of the carabiner, the less chance that your rope will cross under itself and jam up.
It is very hard to evaluate carabiners over the internet. You may want to go to a climbing store to actually get your hands on specific carabiners and see the sizes for yourself, rather than ordering online (at least until you know exactly what you want).
Lock style
Self-suspension is often quite dynamic, and for dynamic applications, using locking carabiners for main support lines is important. For static suspension, non-locking carabiners (such as wire-gate ones) are adequate… but most self-suspension involves moving around in rope, so I suggest investing in adaptable, high-quality equipment from the start. Carabiners that don’t lock can accidentally and suddenly come unclipped due to pressure from the rope inside the carabiner, sudden movements, or colliding with other components of your rig (such as the suspension frame, a body part of the suspended person, or another upline).
I have personally seen an non-locking carabiner come unclipped from five of the 6 rope wraps it was clipped around during a transition/drop – the bottom was very fortunate that it happened to catch on that last wrap, and they didn’t fall onto their heads, although the uneven and severe pressure on a single 5mm strand of rope caused bruising that lasted almost a month. There have been other rope incident reports of accidents caused by non-locking carabiners, as well.
There are many different types of locking carabiners available. I personally prefer a screw-lock, but plenty of people hate screw-locks and prefer twist locks (sometimes called “auto-locks” because they default into their locked position when not being held open). There are also ball locks and a number of other fancy mechanisms. The choice is mostly personal preference. Many people just build their motor skills around whatever type of lock they are first exposed to, and “imprint” on that type of mechanism for the rest of their bondage career. The reason I prefer screw locks probably isn’t any more sophisticated than “it’s what I got used to using when I first started.”
I recommend going to a climbing store, playing with a few different types, and seeing what feels good in your hands. Twist locks have the advantage that you can’t forget to lock them, because they spring into a locked position automatically. If you use screw locks enough, you eventually will forget to lock one. However, getting a twist lock open and holding it open can be difficult (especially if your grip strength is almost burned out).
Models that I prefer at this time are the Black Diamond Rocklock Screwgate Carabiner and Petzl William Locking Carabiners (which I especially like because it shows a red stripe if the carabiner gate is unscrewed). Note that models change and are updated constantly. Expect to pay $10-$20 per carabiner.