While it's not required, it is strongly recommended that the From Email Address on your ReachMail messages be a private domain.
It all boils down to the fact that when you send mail, your domain garners a reputation, good or bad. In most cases, a slightly bad reputation is better than no reputation at all.
There are a myriad of factors that are used to decide your message placement, but domain and list quality are two of the most important factors when it comes to sending bulk email. When you send from a consumer domain like gmail.com or hotmail.com, you effectively don't get the benefit of any accumulated delivery history. A simpler way to put it is that it's just doesn't look professional and you mail will be treated as such.
Bottom line is that failing to send from a private domain is only going to make it harder to deliver your mail to the inbox.
If you have your own website, chances are that you already have an address you can use instead of your free consumer email address. If you don't have one, consider buying one. Google Apps or Yahoo Small Business are just two of the many affordable options out there.
One thing to keep in mind when creating a new private domain, is that any domain that has not been in existence for at least 90 days runs the risk of being flagged by what is know as day-old-bread. A common tactic for spammers is to create new domains to work around a blacklisting. As such, many receiving domains will reject or bulk delivery from newly created domains as a way of catching spammers in the act.
Additionally, using a yahoo.com or an aol.com from address will cause your message to be rejected due to DMARC policies in place at those respective domains. For more information see this blog post. While the post was put up before AOL followed suit with this tactic, this same policy is in place at both domains presently.