Along with specialized uses for email, you should investigate how your users are emailing on a daily basis. Email has come a long way in 40 years and the way people use it has significantly evolved. That's important because it will impact the tools and features you need to look for in your hosted email provider's client software. Sure, Microsoft Outlook is still the most popular on-site email client, but a fast-increasing number of today's email users are opting for other email clients, such as Thunderbird, or all-web clients, such as Google's hugely popular Gmail. These clients can be very sophisticated and, depending on what your users are doing with email, they can have a big impact on your day-to-day business process.
In terms of security for its hosted email services, you'll find this is all hosted in Microsoft's data centers. That means you'll have all the same security benefits as those provided to other Microsoft Office 365 users. Your email data will be encrypted in transit and at rest using SSL and Bitlocker technology. Per Microsoft's publicly available terms of service, Microsoft employees only have highly limited access to your data and only under specific, audited circumstances.
You can also purchase Secure Sockets Layer certificates (starting at $69.99 per year), the software that's represented by a green padlock in your web browser when you visit, say, a financial institution's website. If you plan to sell products via your website, consider an SSL certificate an essential purchase, as it safeguards the data exchange between a customer and your servers.