These are songs that I use when introducing newcomers to tango because I feel that these selections help activate the tango rhythm and stimulate the connection between the couple.
The first two songs I use to warm up and activate the tango rhythm in my body are:

"Milonga De Mis Amores by Francisco Canaro from the Album titled: Grandes Del Tango 29 - Francisco Canaro 2"

"Milonga Sentmental by Francisco Canaro from the album titled: Milonga, Vieja Milonga"

The next five songs are from the album titled Poema (Orquesta Francisco Canaro) which in my opinion are very romantic and help stimulate the connection between the couple:

"Alma del Bandoneón"

"Sueño de Muñeca"

"Poema" - Is my favorite because I was inspired by the connection between Javier Rodrigues and Geraldine Rojas in this beautiful tango in the Milonguero style:

Also on the Poema album, and for the same reason, I like to practice to:

"Tu y Yo"

"La Copla Porteña" There are parts of this song that allow me to really play with many combinations of the Cruzada (With legs crossed) and the Ocho Cortado which is useful to dance in a reduced space.

Once you have mastered the Milonguero style of tango you will be in a better position to branch out into the Nuevo style of tango. Here is a tango also danced to the song "Poema" but in the tango Nuevo style. The couple is Chicho Frumboli (The Godfather of Tango Nuevo) and Eugenia Parrilla:

The Poema album has other good tango pieces than what I mention here. I and am getting more than my monies worth out of it because I play it at practicas and use it to teach beginners.
I definitely recommend buying the whole album: