PHPlist (the mailing list app you rejected) is probably going to be the simplest way to go, if you don't want to write a bunch of custom PHP code. One thing to keep in mind is that you need to "throttle" your email send rate to maximums of 500 per hour (some people will tell you 600 or even 800 -- no one at LP seems to be able to speak authoritatively) and 20 per minute. PHPlist can do this, but not all other mailing list programs can do it.

If you want to go the custom PHP code route, you'll need to write a script to get the newsletter from a file, get users from a file or database, put out the appropriate email headers (including the HTML flag), output the newsletter (including any per-recipient customization such as "Dear Mr. XX," * , and send it off to the mail() function no more often than once every 3 seconds. Probably easier to use PHPlist.

* Back in the early '80s, the Republican Party sent a fundraising letter to the Assemblies of God Church in some Texas city. The letter opened with, "Dear Mr. God,"...