Most common "rr" sound in Brazilian Portuguese?

[Deinonysus]

I have been trying to get acquainted with Brazilian Portuguese and I have heard there are a few ways of pronouncing the "rr" sound. I have been hearing it as /h/ from most sources, but I was doing a Pimsleur lesson today and I heard the initial "r" of "restaurant" pronounced as a very strong /ʁ/ as in the French version of the same word.

Is there a particular pronunciation that is the most common or the most non-regional? Is one of them a bit dated or is it just a dialect thing?

[白田龍]

The initial r- and middle -rr- are pretty much uniform in Brazil, you can say /h/, but with some varying degree of throat friction added to it (like a spanish "jota", but lighter).

I'm native brazilian, and I usually add none or very little throat friction, approaching the /h/ sound, but if I'm trying to speak more clearly (like reading aloud) more throat friction is used. When speaking naturally it varies at random, I'm not usually aware of it when speaking of listening.

In the final and post vocalic position ("-r"), however, there are many regional variants. A strong throat sound here is distinctively marked Carioca accent, which you would want to avoid, unless you will be staying in Rio. You will probably want to use a light apical -r like that wich is common in São Paulo, or an /h/ sound with a sublte throat friction. This sound has many variations, even the same person will vary a lot. Dropping it altogether is also very common, especially on verb infinitives, the final r is probably most often not pronounced.

[tastyonions]

Most common for the double and initial R is probably the voiceless velar fricative: https://en.wikipedia.org/wiki/Voiceless_velar_fricative

A uvular fricative (especially voiced) or alveolar trill is generally more characteristic of Portuguese from Portugal.

[Dragon27]

Luciano Canepari describes (in 11.9) this consonant as 'voiceless uvular approximant' (which concurs with the description by 白田龍 above - "like a spanish "jota", but lighter" - if we describe the Spanish jota as 'voiceless uvular fricative'). Official IPA, unfortunately, doesn't have a special symbol for this sound. There's also a lot of variation in the realization of this phoneme in regional accents.