First, I'd check to see if your property management software offers a way to send a mass email or text to all of your residents. Many of them do.
If you want an email service that offers more flexibility and features, my company is a huge fan of
MailChimp
. It's easy to use, affordable, and integrates with all the other online marketing tools that you're probably using.
I would definitely recommend using an email service like MailChimp over sending the emails yourself through Outlook. Email services handle the liabilities that come with managing a list of subscribers, and you'll get way reporting about how many people you're reaching with your messages.
I like the idea of texting apps like RokitNow, too. Like Rokit mentions in their comment, you have to get residents to opt in to receive those messages, but texting can be a great way to reach people quickly.
The third option I've seen work well (although it's a distant third place to emails and texts) is in private Facebook Groups. Facebook is really good at notifying its users when there's something they need to see. You could set up a private Group for your residents, then use that as a place to share your updates. It also gives residents an opportunity to ask common questions in a setting where you can answer them for all residents at once.