Rest Strokes - Apoyando is the correct term - should only be used when the music allows.
That means in situations in which any melodic or chordal accompanying notes will not be stopped by the rest stroke sounding the upper melody, or an 'inside' melody.
('Inside' refers to a melody played on strings between the bass and treble strings whilst simultaeneously playing the accompanying part on the bass and treble strings ).
In polyphonic music, it is necessary to sound several notes at the same time and if the accompanying note or chord uses an adjacent string to the melody, then the rest stroke will stop the adjacent string from sounding.
Youtube any name player like John Williams, Julian Bream, Elliot Fisk, Alvaro Pierri or the composer Leo Brouwer or the astounding Ana Vidović and watch carefully...
You will not see many, if any, rest strokes.
The same is the case if you search for finger-style jazz and blues.
Players such as Joe Pass, Charlie Bird, George Van Epps, Antonio Carlos Jobim.
Also search the brilliant Tommy Emmanuel and watch carefully....you will not see any rest strokes.
It is also the case in finger-style rock and pop guitar.
The rest stroke was in common use when it was normal not to play using finger-nails as it helped to create a louder note for the melody part compared to the accompaniment.
I have seen young students playing Renaissance and Baroque pieces with rest strokes.
Depending on the piece, it can be a completely wrong technique because the rest stroke actually stops the adjacent string from sounding and the main characteristic of those styles is to have at least two separate melodies sounding at the same time.
Rest strokes can be useful of course, but only if the music allows their use.
They are mostly used in single-line passages, or music which has been composed so that any counter-melody, accompaniment chords, or bass part, are not on adjacent strings.
Some teachers encourage beginners to use rest strokes in order to avoid 'slapping' the strings against the fretboard by plucking too forcefully, which is a common issue with beginners.
In most cases, it is not advisable to remedy the problem in that way because it locks the young student into using rest strokes and causes problems when attempting to use the far more commonly used free strokes.
However, practising your scales with rest strokes can be very useful in improving technique.
A well-known example of a classical period piece in which it is possible to use rest strokes to great effect is Fernando Sor's 'Allegretto' from '24 Very Easy Exercises' #22 Opus 35.
It's around grade five level.
Try using rest strokes to play Albeniz's 'Asturias' or Leo Brouwer's 'Decameron Negro' or Roland Dyen's arrangement of Jobim's 'Felicidade' and you will immediately understand the problem!
There is a video example of 'Felicidade' on the homepage of this site, played on a steel string arch top guitar.