Dear, I have a ready made application for the same objective. We are expert in mass-mailing & this is our day to day job.
Sending 3000 mails in a day depends on the size of mails. My developed application can send 50 mails in one push & it waits for 30 sec for the next batch of 50. If the body message will not so heavy then we can send 100-150 mails in one push.
So first i need the body text, which type os mails you want to send only after then i can calculate the best quote for you.
you also can contact me at: mandeepmtech at gmail dot com
For you better idea i put it $100 for 3000 mails, if mail body is not so heavy.
Regards