Cheapest option
Set up wordpress website.
Get WP Plugin Mail Poet. (Free)
Break Your List into multiple lists of 1999. Mail Poet is free upto 2k emails-but they check this by the # of emails in your subscriber list, which can be uploaded, sent to, deleted and next list uploaded sent to then deleted etc. Rinse & repeat.
Set the amount of outgoing emails per hour according to your daily limit of whatever your host allows (Every Host is different so you will most likely want to find one with higher limits i.e. bulk email friendly. )
This would be the cheapest way.
Or if you are looking for a bullet proof option (which does cost some money but is one of the most powerful options around), which you can find details about on the website in my sig.
But as they say, "You get what you pay for, the rest is all done by hardwork".
