There is no need to reinvent the wheel. Since you've already installed Ubuntu Linux, I suggest using something like the following:
Install Postfix or any other MTA. Whatever comes with your Linux distribution is probably fine (Postfix, Exim, even Sendmail).
Install mailing list management software. For example, Mailman is quite popular.
Then you create appropriate lists, e.g. "students", "teachers", "board", etc., and send email to the list address. The mailing list software is responsible to email individual users, process bounces, can handle subscribe/unsubscribe if needed, etc.
Please be warned: configuring and maintaining an email server looks easy on the surface, but in fact it's an arcane art and there are many subtle gotchas. Outsourcing this task to third-party services, like MailChimp, is not such a bad idea. Not sure if MailChimp has right set of features for you, but there are many mailing list services, and considering that you have very low-volume list, it should be quite cheap no matter which one you choose.