Oracle Database Discussions

My team is developing a client/server Windows application that
utilizes a Oracle 8i database running on a Sun Server with
Solaris.

How should our aplication manage its connections to the database?

We would like to develop a "disconnected" application, where it
would open a connection, retrieve the data (or execute a
statement) and close the connection just after that, holding
connection resources for the least amount of time possible, so
the database could serve as many users as possible.

I4ve been told that this could be very costly to the database
(opening and closing connections all the time) and that we
should rather open a single connection when the application
starts, keep it open thru the application lifetime, where all
sql commands would use this same connection, and then close the
connection when the application ends.

So, what is the best way to go?

Thanks a lot,
Demetrius