Time sign, are given to stress where the " accents " and how the music may be allocated time wise -- for e.g
An octave has 8 notes ( 2 bars of music-- lets take a 4/4 sign. this is now implying that there as an even distribution between each note .
In the octave , we have the ascending bar and the descending bar ( you can in many cases, here it "climb" and fall )
The dominant notes are usually the 1st and 3rd.
One tends to find more simplified rhythms in the " smooth " side of dance .
Now-- we divide the notes into 3or4 values -- A whole note-- a half note-- a quarter note and even an eighth note
Commonly called a Quaver-- a semi quaver-- a demi quaver and semi demi quaver, and so on.
By this method, we can determine how our Slows and quicks may be "time " allocated .
The latin rhythms are far more complex .
reason ?-- many syncopations are present in the very early stages of learning-- this leads to some "odd " time allocations like 3/4 notes etc.
if one delves into the more authentic Latin rhythms ( polyrhythms ) many of the instruments are given very specific roles to play.
the clave, is the one that sets the style--- whether Rumba clave or Son clave.
Dont want to get you too confused--- might i suggest you find a teacher who understands composition and its relationship to dance .
You asked what instrument to listen to for guidance-- that depends on the dance and the arrangement -- For smooth-- the 1st beat of the bar is usually very dominant-- could be piano-- bass -- drum .
In latin , Piano is frequently dominant--- but could be Clave- bass -- congas or cow bell .