Can you recommend a base hardware specification to support 25 to 100 users?

Please see system requirements for a single Zimbra server installation and for a multiple Zimbra server installation. For a basic system, Agileware recommends minimum of 8GB RAM (ideal 16GB RAM), Intel x64 3GHz+ CPU, 2x300GB+ fast hard disks (SCSI, SSD, SAS 10K RPM) in a RAID configuration of RAID0, RAID1 or RAID10. RAID5 is not recommended due to poor write performance. When choosing disks for your server please read this section on Zimbra disk recommendations. Hardware requirements will increase based on load, type of usage and other software running on the system. We recommend software or hardware RAID for email systems and a daily backup regime. Recommended reading, Performance Tuning Guidelines for Large Deployments and Performance Tuning Guidelines for Single-Server 100-500 User Systems

Does the Zimbra server have to be taken offline to do backups? Is there any way to do a live backup?

Zimbra backups are performed LIVE, the server remains operational and accessible, this is a unique feature of Zimbra Network Edition. Zimbra Open Source Edition does not have the same backup/restore feature. The Zimbra full backup process places the account’s mailbox in maintenance mode to temporarily block mail delivery and user access to that mailbox. and Returns that account’s mailbox to active mode and moves on to the next one. For more details see the Zimbra Administration Guide.