I'm brand new to CC. Email authentication seems like a good idea. Is it preferable to use our own domain or simply use the one provided to by Constant Contact? Is one better than the other? We currently have an Exchange server for our email.
Welcome aboard! We have an excellent email sending reputation, and you will be using our servers to send mail, which is one of the main components mail clients look at when choosing where to deliver mail (inbox, junk, or not at all). Using our authentication or your own is really more a matter of preference than anything else--unless your domain has a poor sending reputation (lots of spam complaints, sending to dead addresses, etc), I would expect you to have excellent deliverability using either method.
The biggest distinguishing factor will be whether you want to build your domain's sending reputation and whether it's worth the extra work setting it up to do so. If you choose to send from your own domain and self-publish, you'll want to get in touch with support and have the self-publishing information I'm linking to here available.
Also, here is a helpful overview of authentication that also has links to more in-depth information.
API Support Specialist