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?
GoDaddy hasn't traditionally had an uptime policy for its older CPanel email. But since the company has transitioned to Microsoft Office 365 for its email services, it's now able to enjoy Microsoft's 99.9% uptime guarantee. However, be aware that GoDaddy has replaced the Office 365 health services dashboard with its own internally branded version. It shows the same kinds of information including when the last issue was, and whether or not it's been resolved.
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.
If you don't want to spend a lot of money on web hosting, shared hosting is the way to go. This form of cheap web hosting places your website on a server with other sites. So, yes, your site literally shares server resources with others, hence the tier's name. This means that it's far from the most powerful web hosting type, however. The sites sharing the server compete for resources—everything from throughput to storage space. You'll want dedicated or virtual private server (VPS) hosting for muscle if you expect big traffic, or if you want to insulate yourself from big traffic spikes.