Do you prefer to teach the escape or counter or how to apply/put somebody on a hold?

I think it all depends on what you know, what the situation is , how it reveals itself, and how you choose to react.

Escape is great, holds are great, strikes and counters are also great.

Whatever you feel comfortable with I suppose, and again what the situation calls for.

I think the key to countering an attack is understanding how it works. Because of that, one should get instruction on the basics of the move first. If you know the mechanics of an arm bar, for example, it becomes easier to see where it can go wrong.

For self-defense, there are only a few holds one really needs to address; training against a reverse triangle choke, for example, would be a waste of time if you're defending against the common attacks in the real world. But yes, I believe having a competent understanding of the hold helps understand how to break it.

Your question is all over the place. It is unclear exactly what you are asking. Reading the answers, the the first one by Byron is in line with what I tend to do. If teaching a self-defense class the time is limited so there is no time to teach the students how to properly apply techniques and then how to properly counter them. I will teach them the simplest ways to counter chokes and things they are likely to encounter if attacked. If you get to technical or to advanced the students will learn nothing of use to them. false confidence can be more dangerous than someone that knows they don't know how to get out of things.

When teaching a regular martial arts class, I teach students how to apply techniques. At some point after they begin to be able to actually those techniques in a real situation, I start teaching them how to counter the techniques I have taught them to apply.

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When I initially teach something I first like to let students learn that thing and develop their understanding of it and them have time to practice it. Once they have done that then I teach counters to it or ways of defending against it. This way a student or fighter has an understanding of the technique and has developed their ability to apply as well as use those aspects of countering it or escaping from it when that technique is applied to them. They then also better understand when their adversary is doing something to counter what they are doing or making an attempt to escape from it. Here again knowing and understanding that last thing can nullify a lot of times that counter or escape your adversary is attempting to use.

In some ways its like fishing and I use that as an example when fishing for pan fish. You want to give your fishing pole a slight upward jerk when you get a bite to better set the hook and keep that fish on your hook. Its the same when you apply something and you want it to be successful and effective and them not be able to counter or escape from it until you are ready to let them out of it.

I beleive in a strict, "there is no 1st strike in Karate" so like to train how to get out of bad situation, the worst the better and never from a ready position. If aggression comes at you quick, you will not be able to prepare for it, chances are you will not see it coming. This also leads to my preferred methods of escape which are break the first thing you can that will make the attack end quickest.

In order to understand the weak points that would let you counter a hold, you must understand why the hold works. They are the yin and yang. However, I do tend to teach getting out of some common holds and attacks without explanation of these finer points early on in training because I want to give students some practical options to get themselves out of jam (as an attacker doesn't know that he/she is supposed to wait until the students are sufficiently far enough along in their training!).