What you are asking for would take a book to explain, and although I'm a
very patient person, it would be poor use of our joint time.

With those requirements just for starters, I suggest you consider using
an accounting program that keeps track of jobs, clients, activities,
because when you use one of those you also get all the relevant
functions thrown in that you are going to need but don't know it yet.

Not knowing what country you are in makes it hard, but for example,
MYOB's Accounting Plus program includes time billing which will do all
the things you mention, plus all the rest, and is very good value for
the functionality. A search around "accounting software" and "work in
progress" or jobs should get you started.

Regards
Mike (MYOB Consultant)
Mike