1. The presentation video, letting me understand the following:

Teacher is a positive, pleasant, educated, and communicative personality. I can imagine to sit with that person in a café for hours talking about anything and everything! That's the really important element!

Teacher has a good accent. When I decide for a particular variant of a language, then for me only this accent is acceptable during the learning phase. I really can't stand that silly multi-accent-mix learning courses that pupils are harassed with nowadays. So e.g. English first-year-beginners are confronted (simultaneously) with British, Australian, American, Indian and even German and Japanese accents... Believe me, such textbook CDs exist, and are used in real classes.

E.g., for me personally, English must be British RP, French must be from France, Portuguese from Brazil (paulista accent), Urdu must be Mufarris style, Hindi must be sanskritized Shuddh Hindi and so on. I don't say these accents and styles are better than others, but I believe that it is important to choose an accent and style from the beginning, and to stick to it.

And the teacher should speak different languages, all of them with an decent accent.

2. Pupil/Lesson ratio. A high rate of one-lesson-only students is a warning signal.

3. Feedback. I read everything. Even though the feedback generally is positive, there are different shades of positiveness which can be discerned.

4. Price. The least important criterion. My lifetime is too precious to be wasted in bad lessons with incompetent teachers. So, when I find a teacher meeting the above-mentioned criteria, I usually book the lesson. I am not a rich person, but I would not let a difference of a few dollars prevent me from choosing the best teacher.

I would like to add something which I forgot in my last post. It is not something that I systematically do, but still I do this often enough.

Good teachers are always also good learners. And it is very often helpful to look at their profiles and see the teachers they have been choosing to learn from themselves. So, when these teachers have teachers that they are having lessons with on a regular basis, I consider this a very good recommendation.

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I look at a few things. I check the schedule first now because I often find teachers who seem perfect but then our schedules don't line up. I then watch the video and read the text.

I do look at reviews but only to see things about the connection or if the student even says that the class was great, I like to see why because if I read things like "it was a great class with drilling exercises" this is something I don't like, so even though most reviews are positive you can still take away from them. 

Regarding price, usually, this depends. I can't afford super expensive since I learn multiple languages and it starts to add up. Though I will spend more if the teacher is offering that bit extra like something I won't get from other teachers. Expensive for some isn't for others it is all relative to what you personally can afford.

Though I will say, the US dollar is really bad for the Australian dollar, I think it is currently at .68 so I have to add a third on top of the price. I'm guessing currency changes affects others too, including teachers whose currency is not actually the US dollar. I'm not complaining just pointing out this is something I take into account when looking at prices.