What do you call a guy who talks so elegantly, when he talks he knows what he is saying; he takes care of each word out of his mouth, his words shows his high personality etc ... and what would be the adjective for such words said? e.g. "thoughtfully put", " elegantly said" etc ..
I'm not sure there is a single word which would capture all the nuances which you are after. Precise probably comes close, but has overtones of pedantry (which I think you don't want). Some combination of precise, articulate and sensitive might be what you are after. I would agree with you that eloquence probably veers more into the realm of artistry-with-words than you would like.
I'll be offering a fastidious speaker
Garner on Language and Writing: Selected Essays and ... - Page 516 Bryan A. Garner - 2009
To select one of several examples, in the days when aggravate was first coming to be widely used for "irritate, annoy," the fastidious speaker or writer could either combat the word's debasement and use it correctly or seek refuge in exacerbate.
as well as an*l (sorry, but ...)
Also, more positive:
Adam Smith: An Enlightened Life Nicholas Phillipson - 2010
... thus bestows upon the whole species those names which it had been taught to apply to two individuals.' In the same way we say of a great orator that he is a Cicero or a great scientist that he is a Newton.
silver-tongued adjective: marked by convincing and eloquent expression “a silver–tongued politician”; see, Merriam-Webster silver-tongued
I like laconic. A laconic person's speech could be described as concise, fastidious, precise, or my personal favorite, economical.
(Of course, you could bellow, "This! Is! Laconia!" if you wanted to make an obscure joke.)