A physical (HW) server is indeed 'a server is a computer to run one or more services as a host on a network'.
However each SW 'service' is also know as a server eg Apache is an HTTP server/service.
IOW 'server' has more than one meaning
Its a very good idea to have a dedicated server box that is not also a client wkstn.
For a business, it depends what services you need to run; it's entirely your choice.
Likely options include (but not limited to)
1. mail
2. centralised file storage, thus simplifying backups/restores.
3. http if you want to host your own (externally visible) website and/or eg an intranet website for internal docs, wikis etc.
NB: for security, it may be best to have the external website on a separate box
4. you may want a DB for eg accts, HR, invoicing etc; usually with an http front-end
etc etc...
If you want paid phone support, you could go RHEL. If you can do your own support, try Centos (free rebuild of RHEL)
This (RHEL/Centos) is a long term distro
http://www.redhat.com/security/updates/errata/
The point is what do you want to do with it?
You may also want to have it hosted for you, rather than at your own office.