This is by far the simplest type of emotes you can use on twitch as they are available for everyone and are the standard keyboard emotes you may have used while texting or talking over the internet. Even though they are some of the simplest emotes, they are still used a uprising amount, and especially ":)" AKA "smile", and "D:", usually just referred to as "capital D colon". Some more examples are ":p", ":D", etc. For more on why these simple emotes are still relevant in twitch chat click the button at the bottom of the page to go to Memes and Meta page.
Global Emotes are typically the foundation of basic communication in Twitch chat, they are available to everyone and are some of the most commonly used emotes in chats across the platform. Knowing the meanings behind these are a great start to being able to use Twitch chat to it's fullest potential, and it can be especially useful for getting to know subscriber emotes, as many of those are variations of "classic" global emotes. Global emotes also have their own meta to an extent as some are used much more frequently than others, for example "LUL" being a very prevalent emote (top right of image), mainly based on it's utility and flexibility to be used in many contexts. For more information on the meta/usage of Global emotes click the button on the bottom of the page.
Each different type of emotes are essential to the foundation of Twitch chat but out of all the types, subscriber emotes are what make each individual chat and community unique and provide great opportunities for creative emotes and memes. This is truly where the emote "meta" comes from as each streamer will has their own certain number of subscriber emote slots that they have the option to fill up with existing emotes or create new ones, sometimes by themselves or by a designer. By subscribing as a viewer for the 5$/month you will unlock all the subscriber emotes and be able to use them in other streamers chat as well. If a lock symbol appears on them like shown here, then you have not subscribed and unlocked them yet.
Memes and Meta
The last type of emotes, and probably the least common, are Turbo emotes. These are emotes unlocked when you subscribe for $8.99 to the monthly Twitch subscription program called Turbo (different than subscribing to streamers). This subscription unlocks multiple things including ad-free viewing, a chat badge, custom chat username color, extended broadcast storage and the ability to unlock new sets of emotes, either glitch or monkey. (Glitch is currently chosen currently here)
A useful tip, if you only know part of the word for the emote and if you can't find it in the directory, you can do a faster search for it by simply adding a colon before the first few letters and it will give options to choose from like a search engine. Ex. :Kappa
For an in detail emote directory of every emote on Twitch, Check out: https://www.frankerfacez.com/emoticons/?q=Pog&sort=created-desc