Time Machine is fine, and I use it, but the issue you want to consider is that TM backups aren't bootable unless you wipe and restore through Recovery. So if you need bootable backups, you'll have to look at other options.
It is possible to back up via TM over the network, if you have a shared folder on a server. Also, I believe some NAS systems have Time Machine services built in, although I've never used one of those. Keep in mind that a backup could take a day or more (if you have a lot of stuff) if the laptops aren't hooked up to ethernet—so you should get an ethernet switch to hook your server and your laptops up to.