The best way to use PuTTY, is to use it with Pageant:
Start Menu ⇒ Putty menu ⇒ Pageant (this will just put the Pageant icon in the rightmost part of the taskbar, the icon may even me masked)
Right-click on the Pageant icon and choose:
New session to define a new server you want to connect to
Recommended settings:
Saved Sessions to connect to a server
Add key to select a private ssh key and type/store the matching pass phrase (if you have a private ssh key you generated on Linux, you need to convert it with Putty Menu ⇒ PuTTYgen)