Is there in the books or on Tolkien's letters a description of Sauron's armor during the first or third age, when he was not trying to "seduce" other races?
Is it accurately portrayed in the movies?
There's no description of Sauron's armour in the books - in fact, there's no indication that he even wore any.
The most full description of Sauron is in Letter 246, and reads as follows:
In the First Age, he wasn't an armoured giant but rather a sorceror, a wizard, a necromancer, even, and is described as such in the Silmarillion:
The depiction of him in the movies is an invention so treat it as fan-fiction. In general Tolkien himself doesn't go into this kind of specific detail with many of his characters.
There's an entry on Sauron's appearance at http://www.glyphweb.com/arda/faq/sauronshape.html with a lot of quotes from Tolkien's writing, seems like a well-researched site so I doubt they missed any detailed descriptions...from this, it seems Tolkien was never too specific in his description of what Sauron looked like, and said nothing about what he wore. But in support of his general appearance as a very tall humanlike being, there's this quote: "Sauron should be thought of as very terrible. The form that he took was that of a man of more than human stature, but not gigantic."
Let's begin with the only image Tolkien ever produced of Sauron, as far as I know. Tolkien made this unfinished sketch of Sauron.
This looks almost nothing like the armor we see in the movies. But other images from the films bear no resemblance to Tolkien's sketches either. Compare Orthanc in the films to Tolkien's sketch here:
The armor Sauron wears in the films is based on Tolkien illustrator John Howe's illustrations (for The Silmarillion) of Morgoth, not Sauron.
From the LotR wiki:
One of Howe's paintings of Morgoth:
Howe is well known for illustrating Tolkien's work, but his depiction of Morgoth may itself be inaccurate- as far as I know, plate armor never appears in Tolkien's narratives; everyone wears chain mail or leather armor.