The bottom line is that if you have paid money to own a domain then you should, at the least, buy from a domain registrar that offers email forwarding for their accounts (we prefer Namecheap who do include free email forwarding). You can also create a domain email address from the cpanel given to you by your hosting providers—they’ll also provide at least one free email address for your account.
The basic EAI concepts involve exchanging mail in UTF-8. Though the original proposal included a downgrading mechanism for legacy systems, this has now been dropped. The local servers are responsible for the local-part of the address, whereas the domain would be restricted by the rules of internationalized domain names, though still transmitted in UTF-8. The mail server is also responsible for any mapping mechanism between the IMA form and any ASCII alias.
Syntactically correct, verified email addresses do not guarantee that an email box exists. Thus many mail servers use other techniques and check the mailbox existence against relevant systems such as the Domain Name System for the domain or using callback verification to check if the mailbox exists. Callback verification is an imperfect solution, as it may be disabled to avoid a directory harvest attack.
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?