Hi
As a Linux fan, I'd naturally say Apache but IIS would have adherents too. I suspect the majority of Moodle sites run on Apache so why not join the club?
Re Backup/restore, do you mean the built in Backup in Moodle? I tend to find a database dump and copy of all data files more satisfactory as an admin and also quicker to do a blanket restore.
Our systems run a CRON job on Linux to dump databases and copy data directories in the early hours daily. Has saved my life on several occasions and particularly when someone once hacked our server!!!
If you use MYSQL database then the command 'mysqldump' will do the job nicely.
Another nice spin off is that I run the VMware virtual machine tool on my notebook and can 'clone' any server quickly locally for experimentation and/or backup/restore of individual courses without touching the running system. Well worth it! http://www.vmware.com/
Regards
Alan