Business email plans have limits, so check the amount of messages you can send daily and how many recipients you're allowed in a single mailing.
We use the standard PHP sendmail on our server.
You'll also find suitable packages at ionos.com, dreamhost.com and polarismail.com. IONOS offers 50GB user accounts in bundles. The best savings is 10 addresses for $25. With Dreamhost, you can get accounts for less than $2 per user, and their Unlimited hosting plan lets you set up as many accounts as you want, and whatever domains you have. But they are also touchy about exceeding their daily message limits and the amount of messages you can send at the same time. If your forum sends announcements to, say, thousands of recipients from a single mailing, you are apt to exceed the guidelines of most of these providers. That's not what they are suited for.
It's worth checking first.
As to problems with blocked accounts, you sometimes need to contact the mail services that are doing this (Microsoft Hotmail/Outlook and Yahoo are among the worst offenders) and use their site to file a request to allow messages from your host/server's email system. That's what I have done.