Limit number of outgoing messages in postfix

You could use the deadbeats trick:

main.cf:

transport_maps = hash:/etc/postfix/transport
deadbeats_destination_concurrency_limit = 50

master.cf:

deadbeats unix - - n - - smtp -o smtp_connect_timeout=5 -o smtp_helo_timeout=5 smtp_connect_timeout=2

transport.cf:

hotmail.com             deadbeats:
yahoo.com               deadbeats:
earthlink.net           deadbeats:
freemail.com.au         deadbeats:

Since you're running Ubuntu, you should be able to get a functional postfix setup by running

dpkg-reconfigure postfix

This should run a dialog that asks you a series of questions. One of the questions will be along the lines of "Other destinations to accept mail for", to which you should reply with an empty string (i.e. blank). You should also be certain to give a valid email address (e.g. yours) in answer to the question "Root and postmaster mail recipient", so that mail generated by the system by/for system users gets delivered somewhere.