any distro will come with apache pre-installed or easily available through the package manager.
-host our website - most important thing
Again same as above. For the stats they're mainly PHP and MySQL based anyway and some are available from package managers.
-host a few other sites maybe - So the usual web hosting software like MySQL, PHP, statistics etc
-ftp server for uploading websites
Samba isn't too hard to setup and again comes with nearly all distros.
-have some sort of shared folders - samba shares etc
Amanda (overkill probably). BackupPc aint bad, but I just prefer using cp.
-some sort of backup solution - been looking at BackupPc (views?)
cp -frup /original/* /backup/
Zimbra? Maybe overkill?
-Possibility for an email server
OpenSuSE has yast, it's handy though I've found a couple of niggles with the iscsi module.
-I also need some sort of control panel as they make everything so much easier - I've tried webmin so far and it seams quite good, but some views on others would be nice.
It's down to personal preference really. My preference? Fedora. I would probably recommend OpenSuSe for you since you can configure your stuff quickly with yast.