The first thing I have to say to everyone who asks me to design a backup solution is "what's your recovery solution? what are your recovery needs?". Then design your backups around that. Don't back up anything that won't be restored. You have to protect against both disaster recovery (loss of total system) and operational recovery (file deletion, corruption, historical trails). DR for a PC is usually from a stock image; OR for a PC can be managed through much better methods than PC backup.
The only thing I do at work all day every day is backup. I'm certified on one of the major commercial backup applications, two purpose built backup appliances from different vendors, and have formal training in a few other commercial applications. We have a team of 6 that manage backup for the company's data internally, another team of 5 that manage backup for our IT customers, and a couple of part-time backup admins for rogue corporate business units. We have an offshore team of 12 that support backup & storage for both internal & external 24x7 (max 3 on shift at any time). Internally our biggest backup server runs 10,000jobs/day for 1300 hosts; across all internal servers it's something like 25,000 jobs on 4,000 host. I spent almost $1M in capital this year just to refresh EOSL backup infra, and have asked for $3.1M next year to get into the 21st century for all our backup storage. My colleagues have spent at least as much in growth this year. Across the enterprise we protect 12PB of front end data. Globally we are considered a small customer to our backup software/hardware vendors. We don't do endpoint protection because it's not worth the effort.
If you really are going ahead with what you've described (I suggest you don't), then my biggest worry would be software & config deployment during version upgrades, OS re-installs and infrastructure changes. If you add another backup server are you going to have touch every PC? If you upgrade your server to a version that drops support for a given client version and the user doesn't bother upgrading can you push it down? Can you make sure it gets pushed the next time he logs in?
If you have any remote users, use a tool that does client side deduplication and incremental forever with synthetic full backups being hydrated on the server.
Know what your requirements are for portable media, and make sure the tool you use includes/excludes it as per corp policy. Will rsync of / pick up /cdrom? Set the users expectations appropriately and communicate with them what they can expect of you. Make sure everyone knows where their division of responsibility starts and ends, and make sure there's training material available that aligns with those divisions.
That said, if you really are a big company, then forget the endpoints, put your user's data on LAN shares, SharePoint, Exchange, etc and protect their data using server backup. Encrypt the endpoints in case some PHB decides to not use the LAN shares and stores corp data locally, but if he didn't put it on the LAN as per corporate policy, then let him sweat it out for losing his data when the laptop gets stolen/dropped/dies/etc. I have no sympathy for anyone that doesn't follow documented policies & procedures. They all get the stock corporate image, which gives them a personal and a team share. I don't even cheat like some of my colleagues, my laptop is not backed up to our backup servers and I've had it replaced/reimaged every 2 years or so. I keep my historical PST files in two locations. Two hours of setting up my windows preferences or importing app settings from dumps I put on my home drive and I'm back in business. Data doesn't belong on PCs - I wish they were all dumb terminals and any machine you log in to mounts your home drive, runs apps off shares or in remote sessions, and your profile follows you around. Or follow the mainframe strategy and RDP into your desktop / use VDI.
Anything less than 20 endpoints I'd consider small, go ahead and use simple tools like rsync. More than 20 you need an easy to deploy, intuitive to use background service that connects with a central backup server that manages everything from schedules to include lists and retentions. Give your users a point & click interface to run manual backups and restores (or don't, and all restore requests come to you [which sucks because you can't do your job and live your life if you're always working on someone else's problem]). Use software that controls access so that only the user/machine that made the backup can pull down a recovery - you don't want the night guard pilfering the CEO's data just because he knows how to spoof an IP when the CEO's offline.
I can't recommend a particular OSS or even free closed tool that is, what I would consider, good enough for big business. I played with Amanda/ZManda very briefly a few years ago but configuring the rules was less straightforward than I anticipated. Veeam was mentioned earlier and their commercial product seems to have a decent reputation so their free product could be worth considering. All the rest that I could speak about are not centralized and/or have way too much administrative effort to provide users with the level.
Lastly, don't forget - nothing is free. Open source software may not have any licensing costs but in my experience requires more internal support than a well built commercial offering or even service provider. There are a lot of products out there where the client software is no charge and you just pay the service provider a few cents per gig.