Always after the trigger, but you don't have to wait for enemy to complete their intended movement
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.
A reaction always occurs after its trigger unless a rule specifically says otherwise.
Thus, your readied action would take place after your enemy moves the specified distance.
It is fine if the attack comes in the middle of the enemy's intended movement just as long as the trigger has been satisfied. There is no rule that says that movement must be completed as a block and that nothing can interrupt it. On the contrary, the player can break up their own action in any number of ways. Thus, it is very reasonable to say that enemy reaction can also trigger in the middle of movement as well. Just like an opportunity attack, once the attack has completed the enemy may continue moving if they are able.
- Immediately after the enemy has moved 10 feet, you may take your attack, even if they plan on moving more.
- Immediately after the enemy moves at all, you may attack.
Minimum movement should be 5 feet on a grid
If you are using a grid, I would recommend breaking up the movement into 5 foot chunks especially for things like the second trigger since since that is the smallest tactical movement the rules are really able to handle.
If you are not using a grid, then timings are obviously a bit less precise so just allow triggers whenever, narratively, the character has moved a significant amount.
You can ignore triggers as well
It is worth noting that you may ignore any number of triggers but still choose to react on a later trigger as long as it is before the start of your next turn. For example, for your case 2, once the enemy moves 5 feet your reaction would trigger (assuming they were in range), but also every 5 feet thereafter until you choose to act on it (as long as you don't use your reaction in other ways and it is before the start of your next turn and the enemy is still a valid target for attack).
As Jeremy Crawford has said:
Ready action. The rules says you can ignore the trigger, because yes, you can ignore it. You can try again if it is open-ended enough.
Most of the time, it is going to be better to keep your triggers more open-ended
Since you can ignore triggers and still use them later in the turn (assuming you worded the trigger to not exclude that possibility) there is no real reason to be super specific when you word your triggers. "When the enemy moves towards me" triggers much more often then "After the enemy moves 10 feet" and you make no sacrifices in choosing it over the more specific one. As long as you word things the way you want, you should be able to make do with a more general trigger in most cases.