Yay! A fellow Aganos! 
Well, you can break on auto-doubles (easy difficulty), manuals (hard difficulty), or linkers (medium difficulty). Openers are out of the question, and enders can only be broken if it’s an opener ender combo. You can also break any combo that doesn’t have a break opportunity in it after the 3rd hit.
I like to break on the ADs, for the reason stated as above. They always hit twice and follow very specific animations for each character that you can learn and memorize. For example, I can tell you that Riptor’s light ADs always attack with her claws (from her arms or her legs), her medium ADs always attack with her head or a bite, and her heavy auto-doubles are always her flames or her tail.
I know this, because whenever I had a tough time in a matchup, I chose my opponent’s character in practice mode (this was before combo-breaker training was a thing), and I would do all of the autodoubles for that character and watch the animations very closely. Basically, I would just sit there and start with a special move (the opener) and follow it up with each of the 6 attack buttons (LP, MP, HP, LK, MK, and HK). Those would show me the animations. Do this for about 10-15 minutes, and you should be able to reliably identify them for combo-breaking.
However, I feel I have to warn you - when it comes to combo-breaking ADs, lights are the hardest because they’re unreactable (meaning if you see them and try to react with a combo-breaker, you’re already too late, as it is not humanly possible to do so - the devs have said this; so, you will have to continue guess-breaking on those). Mediums and heavies are reactable, however, so you can still wait on those. Mediums, naturally, are harder to break than heavies because they’re faster, but the heavies still offer mixup potential and do the most damage if they get through.
Linkers can be broken too, but are a bit harder to determine, because the animations for linkers are often very similar, since it basically copies a special move. With these, you want to pay specific attention to how many times they hit as well as how fast the move comes out. It’s not universal across the board, but generally speaking, light linkers hit once, mediums hit twice, and heavies hit 3x (exceptions include moves like Thunder’s triplax, which, as the name suggests, always hits 3x; also Kan-Ra’s whirlwind linker and Cinder’s flamethrower linkers both hit up to ~10x). This is why they’re harder to break than ADs.
Manuals are the hardest to break because even though they’re often used in place of ADs, they’re faster, unreactable (like the aforementioned light ADs), and only hit once (instead of twice, like the ADs). That being said, they do less damage than ADs (since they only hit once) and you can still learn the animations for them the same way as you can with ADs in order to identify patterns your opponent may be using. It doesn’t matter which strength of manual they do though - lights, mediums, and heavy manuals cannot be reacted to. This means that if you guess break all of the time, you will almost always lose. To combat this, the developers have set it up so a manual can only be of certain strengths based upon the previous linker. It goes like this:
light linker = light manual
medium linker = light or medium manual
heavy linker = light, medium, or heavy manual
So, in other words, if you can identify linkers, you can get an idea of what comes next. For example, if you see your opponent do a medium linker, you know the follow-up manual can’t be a heavy manual, since the game won’t allow it. If they do a manual, it has to be a light or medium, because of the rules above. This helps make the game a bit more predictable. It also gives you more reason to do heavy linkers, even though they’re easier to break than other linkers - because it gives you more leeway on what you can use for a follow-up manual if you choose to.
Manuals however, are hard to pull off, unlike ADs. They take a lot of practice (although I’m happy to announce that they officially got a little bit easier with S3) to do. Even worse, using the example above an opponent can still throw you a curve ball by doing the medium linker in order to make you think he’s going to do a light or medium follow-up manual, only to instead do a heavy AD in place of it and locking you out in the process. This adds to the mindgames of KI and is why the manuals are considerd the hardest to break, and are among the highest levels of play in the game.
Regarding identifying many of these moves, if you’ve got a good ear or a good eye, you can actually tell many of them apart by the sound of the hits they make or the speed of the animations, rather than the animations themselves. Furthermore, you can evil tell which strength they’re hitting you with based upon the animations of your own character (which is actually better to learn if you solo/main 1 character; otherwise, learn your opponent’s animations for the entire cast). The downside to these methods of determining strength is that you often have to wait for the hit in the animation, which delays your reaction time considerably. Since moves are broken down into startup frames (when the animation starts to when it hits), active frames (any time during the animation where the move can hit), and recovery frames (any remaining frames after the move is done hitting and before the animation actually ends), using these methods will prevent you from reacting on the startup frames and only gives you a window that starts at the active frames. Usually, if you’re in recover frames, you’re already too late.
I hope this helps! 
