ShellInABox appears to provide a colored terminal interface to browsers via Ajax. (homepage) Since it runs as a separate webserver, you may need to link your users to a different port on your site. There are surely more alternatives (other projects like this) out there.
The following advice applies regardless whether you use ShellInABox or continue to provide ssh access.
If you don't fully know and trust all your users, then assume at least one of them is a whizzkid cracker, determined to crash or break into your system. The first thing he may try to do is log in and run a forkbomb.
You should therefore do your best to sandbox users, so they cannot harm the system or each other. Restrict their access privileges (file/folder/network access) to only what is needed to achieve the tasks you allow. SELinux and AppArmor have facilities for this. You can find some more sandboxing techniques here and here. Docker is a new system that may be worth investigating.
It would be very wise to host your login server on a separate or virtual machine, distinct from your main webserver, so that any user who does manage to break out of the sandbox will not be on the same machine as your other services. (But note he will still be inside your LAN!) User-mode-linux is a less secure alternative and chroot is worse still, but better than nothing!
If users should be able to save files, then I would recommend giving each user a separate account, especially if their files should persist between sessions. Of course, as a workaround for auto-login you could provide a guest account with password guest555 for all users, but then a malicious user could bother others by deleting files or putting nasty stuff in the shell startup scripts. (I certainly don't recommend guest/guest because crackers regularly scan the net for ssh servers hosting that account!)
