An excellent Q---
Also.. a difficult one, as most well know, the combination of several aspects, each important in their own right, go to make for good teaching..
heres a list, in no special order...
1.. know your subject, and I mean well.
2.. always demonstrate what you are about teach BEFORE teaching.
3... check with previous students ( if poss. ) about their experiences.
4.. check the background of the teacher ( dance wise )
5... go to a milonga or practica (they are socials ) watch.. ask questions .
6..keep an open mind on the style you wish to commence with.. salon is less invasive .
7.. invest in music.. see which appeals to you, and make your style choice upon that ( ask the teacher if they teach the style you chose ).
8... If you have prior backgound in other Tangos.. go in with an open mind, it will challenge and delight you ( and confuse ).. warning.. it can become addictive !
As to Soc. with T.Arg. as an adjunct ( they dont include it with the Standard Div. ) UKA has a complete syllabus designed on the Br..Silv.. Gold premise... it has suggestions at advanced levels rather than requirements.
Paul Bottomer, former World Prof. Champ. has a book published ( Tango Argentino ) that is the most concise ever published.
It may be difficult to obtain.
I have a copy , and will be happy to supply ( here ) any info.on content , within reason.