I have taken up a new job, and I need to undertake some web mapping sing Geoserver. I have no idea the hardware required to install Geoserver and do web mapping. I know there is a server involved, is it the server that will host my installation and the platform ? I can't quite figure out the whole set up yet.
Just start playing!
Get yourself a virtual server (Windows or Linux, whatever you're comfortable with), and install the OpenGeoSuite.
I run a small production server with around 2 GB of ram and two processors and it works fine.
As John Barca says, you can scale up to very big, with load balancing and separate, redundant database servers. But to start with, just a little virtual server will do.
Depending on the job you want to do, if you don't do sysadmin stuff much, something like CartoDB or MapBox might make you more productive, faster, and they handle scale for you.