What musical instruments JS Bach owned and had purchased during his career? Is there any historical information on Handel, Vivaldi, Beethoven, Scarlatti, Corelli, Tartini?
Go to Wikipedia and look up the articles on each of these composers. At the bottom, under "References" you will find bibliographies of well-regarded printed book biographies of each of these composers, as well as books on music history. Hit the library and look them up and read them.
Are you asking about what kind of instruments in general, or about the specific musical instrument makers who built individual instruments for these musicians? Your question is tremendously broad.
Just a couple of quick observations: Bach played harpsichord and clavichord and violin at home, and was believed to own a lautenwerk (look it up). He did not actually play or own a lute, and his Lute Suites as they were originally written out could not be played on a real lute without some changes. They naturally fall under the fingers of the keyboard much better.
Corelli was the first violinist of note, in the world -- the violin was practically a newly-invented instrument at that time. His playing techniques and the limited range of fingering positions (no high notes) were unique to him because he was making up the playing technique as he went along.
Handel played harpsichords.
Scarlatti played harpsichords, but was surrounded by Baroque guitars and guitarists and this influenced his harpsichord playing and composing.
Vivaldi was a childrens' orchestra director and teacher and it's likely he got his hands on and could play practically every kind of instrument available in his day.
Simply because of the years that he lived, Beethoven was one of the first composers to get his hands on something resembling the modern piano and to use it to compose and perform. The piano evolved, technologically, rapidly during Beethoven's lifetime, continously getting larger, louder, with a wider dynamic range, and with more notes on the bass and the treble.
There are fantastic lectures from prof. Robert Greenberg from I think Berkeley. His lectures on all these giant bigger then life composers on the teaching company website. He goes in depth their life, work, and also their caprices. Very informing and a plus entertaining. About Bach he played on the organs of the noblemen that he was employed by. He wasn't a wealthy man in the beginning of his career. If it was his or it was from his employee? The harpsichord.