Which antibiotic is very good for tonsilitis? Why?

Penicillin type. Tonsillitis is commonly caused by streptococcus. This bacterium is sensitive to penicillin and penicillin like antibiotics such as amoxicillin. If you are allergic another antibiotic such as azithrycin may be used.
Depends. There are various throat infections that lay people call "tonsillitis". Simple streptococcal infections still respond to old-fashioned penicillin. Abscesses or recurrent infections may require different drugs, e.g. Cephalosporins, sulfa, or others depending on the suspected organism, course to date, and patterns of resistance in your area. Rarely, IV antibiotics may be needed for severe cases.