I will try to answer to all your questions....
In terms of which distro to use, you can choose any and configure it to your preferences. Since you are a newbie you could start with ubuntu just to get accomodated. You wish to configure a server, therefor you could use some other distros which have proven to be reliable in such case. For example fedora, centos, debian, I, for instance, pretty much prefer gentoo but they all require a little bit of reading before using them. You can find at tldp.org a bundle of documentation which you will find very helpful.
In terms of ease of managemet, I find Linux to be accessible to anyone, depending on the time you are willing to invest in getting used to it. Management can be very easy. For instance you could use a mail server such as Postfix or qmail and manage them from a web based interface (webmin). Or install LDAP or Samba for authentication, respectively file sharing and manage them from web interfaces. So linux can be configured to be very user friendly. Personally, I find the flavour in linux to be working in command line.
Here is a howto on building radius on Linux:
There are software licenses for linux too, but there are also opensource alternatives which are totally free.
As an example for your problem you could use: Gentoo distro, postfix mail server, LDAP authentication, SAMBA file server and Amanda backup suite. As add-on software for management you could add: webmin, phpldapadmin. Regarding disk imaging software you could use unix utility dd.
I am not saying that getting this to work will be easy but after reading some documentation you could end up with a very reliable and easy to manage server which will cost you only in terms of hardware.
As for the VPN, you could check out a little about ipsec implementation on linux and OpenSwan. You can build VPNs on linux. Regarding strictly your question, Linux like any other OS, respects networking protocols, so it will work just fine through a VPN connection.
I suggest you first read some general information like howtos regarding getting started with linux and i'm sure you will figure out from there where to go next.
Hope, this is helpful.