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As for deciding which one to pursue at the start, just go for the closest one, and if the closest changes in the course of the hand, go for the new closest one. If you cant tell what yaku is closest, go for riichi.
Locking in a specific yaku at the start as the one you're 'going for' is detrimental to the majority of hands you will play (although that might not be obvious if playing in lower rooms).
All your number tiles are from the same suit? That's a Yaku.
You have the same sequence across the three suits? That's a Yaku.
All your sets are triplets? A Yaku as well.
You have 1-2-3, 4-5-6, 7-8-9 on the same suit? Sure, a Yaku.
None of your sets have a terminal, or all of your sets have a terminal? Both Yaku too.
To make things easier for myself, I've written a reference table of just the "bare minimum" Yakus - many of them have an upgraded form (like Half-Flush -> Full Flush), but to keep the list concise I just wrote the basic one.
https://steamcommunity.com/sharedfiles/filedetails/?id=3296701453
Keeping track of how much you're going to score is what I'm finding harder, as not only the different Yaku have different values, you also have to consider Fu, Dora, Red Fives, etc. But as a rule of thumb, the most complex the Yaku, the bigger the score - and the Red Fives and Dora help a lot.
The two most common open Yaku to know are:
Tanyao (All Simples) - Only number tiles from 2-8. No 1s, no 9s, no winds, no dragons. Just be careful of leaving a 23 or 78 shape in your hand, you might draw the terminal and get screwed.
Yakuhai (Round Wind/Seat Wind/____ Dragon) - Triplet of the round wind, your seat wind, or any dragon. Once you have that triplet secured, the rest of the hand can be anything. If you have a pair in your starting hand, get ready to Pon, but if you only have one it's best to let it go, odds of drawing more are low and you will slow your hand down holding onto it.
For a new player starting out, I suggest you focus on only these three Yaku. Only ever open your hand for Tanyao or Yakuhai, go for Riichi instead if you can't get those. Keeping it simple like this is a good way to focus on learning tile efficiency for now.
I think you can and should get all the way to Adept rank with just those. Once you've done so, you're ready to learn a few more to add to your repertoire:
Honitsu (Half Flush) - Hand containing only one suit, plus honors (winds/dragons). Good to stack with Yakuhai. If you have just the suit and no honors, that's Chinitsu which is worth even more.
Chiitoitsu (Seven Pairs) - This is a special exception to the usual composition of a hand, instead of four groups of three and a pair, it's seven pairs. Since you can't call pairs, this hand is always closed by definition, and can thus stack with Riichi. But unlike other closed-only hands that I won't bother pointing out because they're all subsets of Riichi, this is one you need to know since it's a unique exception hand.
Toitoi (All Triplets) - Pon-nya! It can be tricky evaluating whether to commit to Pon or go for Chiitoi instead. I generally do not like to call Pon unless I have a triplet already in the hand and three more pairs, or I'm already opening for another Yaku that I'll stack with this. Goes well with Yakuhai.
Sanshoku Doujun/Doukou (Mixed Triple Sequence/Triplets) - The exact same sequence/triplet in all three suits. You often can't force this since a two-sided wait can draw the wrong tile, so it's rare to open for, but be aware of when Doujun looks possible. Don't actually worry about Doukou though, that's exceedingly rare.
Ittsu (Pure Straight) - 123, 456, 789 in one suit. Note that the configuration of the hand must actually use those exact sequences, having those tiles but grouped differently will not count. This is also tricky to open for, beware of multi-sided waits that can invalidate it if they fill the wrong way, but you can sometimes try to force it off a closed wait.
Iipeikou (Pure Double Sequence) - The same sequence in the same suit twice. This is a closed-only Yaku, it will not count if you open, so I nearly left it off this list as it can be considered a subset of Riichi. But it's simple to remember and quite common, so I guess I can list it here. Pinfu is another really common closed Yaku, but it's actually a bit more complicated to remember so uh don't worry about that yet just know that it'll just pop up with your Riichi hands sometimes.
Over time, you'll learn the rest. But everything else is either a lot more rare, or a closed-only subset of Riichi that doesn't need to be explicitly learned yet, so don't overwhelm yourself trying to memorize everything immediately. Focus on the common ones.
https://static1.squarespace.com/static/634a7884c297a25f06589b79/t/63c82bff2245392703c3a3cb/1674062885858/WRC_Yaku_1_5_3.pdf
Studying is the best and fastest way, but it is boring.
just remember the "very common yaku" list and, if you can, the "common yaku", these are the yakus that you'll use 99% of the time