Need recommendations for multi-site AD and file sharing

I've been out of the IT game for a few years, but recent layoffs have me taking on some private clients.

A new one has multiple offices that share many SaaS resources and needs user management and basic file sharing/data backups.

What's best practice in this case. A single domain with a DC in each office and a single file storage location? Is there a simpler and more cost effective solution than buying a server for each office?

Also, to get the servers to connect to each other, does one have to be running web services or public DNS services?