We're looking at using a media server in conjunction with our dedicated Moodle server. Right now, they're on the same server and while we don't serve THAT much media content, it's increasing (podcasts, vodcasts, and other streaming media) as faculty are adopting more modern methods of content delivery. We're not currently using load balancing (we haven't had a need... we've got about 250-350 logins per day with moderate activity on a brand new 8GB quad core server. )
We're looking to offload our "heavy" media from the Moodle server to prevent large backups ("large" being over 50MB per course... there's several different takes on how that should be done, this is just what we've decided). Right now, our course sizes aren't too bad (in my opinion), but there is a lot of content that doesn't "need" to be on the server. By lowering our backup sizes from our Moodle server, we can speed up backups, make them smaller, and decrease our costs to back up all the information we have. Our moodledata backup folder is about 80GB (I keep them a looong way back though) and our moodledata folder is about 5GB.
Right now, we don't have a tight integration with our Student Management System, but we're looking to add it soon to save our distance learning department the headache of entering all the students via bulk upload/enrollment.
We're looking at Single-sign-on, but haven't updated our core code to a new enough version yet (we're on 1.8), but we will be once we've made the move. The less of an inconvenience it is for our users, the happier they will be and the less phone calls I get.
Recoveries/Backups... I'd follow all standard procedures for that, with a err to the side of "paranoid" even though the Moodle system has been quite stable for us (we've only had an issue with Apache and Windows not playing nice). We backup our servers every night off-site. At night, I do a SQL dump of all databases, and I backup our moodledata and moodledatabackup directories and run them as scheduled tasks (via the Moodle Admin area for Moodle specific backups). As long as you've got those covered and you're using a pretty standard install (not a lot of additional add-ins, etc), then you should be pretty well set. I might be forgetting (I'm just doing this off the top of my head). Oh, of course... TEST your recovery procedures from backups that your system is making!! This is critical. There's nothing worse than a backup that fails, right?
Hopefully my ramblings will bring you some information that's valuable. If there's more that you'd like to know, let me know by replying to this forum. Thanks.