Your next major concern will be compatibility. It's not a shock that most businesses run on Microsoft Windows and use some form of Microsoft Office. Being able to use common third-party clients such as Microsoft Outlook can often be a concern, and even today, compatibility with Microsoft Outlook isn't necessarily guaranteed. This is especially true when sending and receiving meeting invites. It only takes one garbled meeting invite to realize how frustrating this can be in the real world. Even if using Microsoft Outlook isn't a concern, portability is. If the service is entirely web-based, then is there a means for me to take my email offline and send email when I connect?
If privacy is your number one concern, perhaps you should go with Protonmail. You can upgrade to an email with your domain easily on a web interface under “Protonmail Plus” or “Protonmail Visionary” plans. However, the plans can be rather expensive, as getting only 20 GB storage space could cost you at least €24/user/month/yearly. Most email hosting providers retain your emails for months even after you delete your account. This Swiss email provider will destroy all your data when you delete your account.