When a caster begins casting a spell, for the purpose of readying an action, can another character identify who the spell is targeting before it goes off, and thus react? If so, which of the components would indicate this? Verbal, Somatic, or Material?
What about spells with range touch vs spells cast at range?
Spells do not have any perceivable effects before the spell is complete except for the casting components. Those casting components can help you identify the spell that is being cast, but nothing else (and only if you spend a reaction to do so). If there are no perceivable casting components, you can't know anything about the spell being cast. Any other information about the spell beyond its basic identity is pure conjecture. This obviously includes information about potential targets.
So, you know they are casting fireball. Great. You have no way of knowing at all where they intend on casting the fireball exactly. You can only guess. Even if the caster is running up to you eyes locked on you chanting the spell's mystic words, you can't be certain that you are the target of a spell. There is just nothing that would be perceivable that would indicate the target until the casting is complete.
(As discussed in At what point does a caster define the target of a spell?)
As you mention in your question, the part of the text dealing with readying the spell is the most compelling piece of evidence the book has:
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs.
Combined with the Sage Advice, Rules Answers: June 2016:
For readying a spell or other action, does the target have to be in range?
Your target must be within range when you take a readied action, not when you first ready it.
Together, these pieces create a compelling case for a general rule.
While readying a spell (per the SA ruling) you can specify the target of the spell when the spell is released not when the spell is cast (related). And, because the description says that you "cast [the spell] as normal" there is solid evidence that that is the normal behavior of spells in general.
Thus, the general rule we glean from this is: a spell's target is determined when the spell is released but after it is cast.
Thus, there is no way to determine the target beforehand because the target is not necessarily chosen yet.
Being the target of a spell is not a perceivable trigger for the purpose of readying an action with the intention of triggering before the spell's casting is complete. If the intent is to trigger after the spell is cast it will work, but not before. As indicated above, there is just no way to perceive the target of a spell with any certainty before the spell is cast.
It is hotly contested right now if any trigger depending on perceiving spellcasting in progress can be precise enough to trigger before the spell is cast. This answer does not provide evidence one way or the other on that general issue. However, this particular method of setting a trigger based off of the targeting of a spell will not work to trigger before the spell is cast regardless of if it is possible for triggers to do so.
See Is it possible to interrupt spellcasting? and Timing of the Ready action when the trigger is associated with spell casting? for examples of other Q&Aswhich adress the issue more generally.
