Personally, i wouldnt be running Fedora or Ubuntu in a server environment, as they are both a little too bleeding edge, and the frequency of updates MAY break things.
Any of the other distro's are a good choice, my personal preference is CentOS, and for all intents and purposes RedHat and CentOS are the same. Except for release schedule, and support.
There are a number of ways you can setup networking in VirtualBox, but by default, you should be able to directly ping from the Win7 box, to the VM once you install a distro. If this works you should be able to access the webserver once its installed/configured.
You wont HAVE to install putty/ssh as you can directly access the VM through VirtualBox.