If you want easy and simple, you might also want to look at Fabric. It's an automated deployment tool like Ruby's Capistrano, but simpler and of course for Python. It's build on top of Paramiko.
You might not want to do 'automated deployment' but Fabric would suit your use case perfectly none the less. To show you how simple Fabric is: the fab file and command for your script would look like this (not tested, but 99% sure it will work):
fab_putfile.py:
from fabric.api import *
env.hosts = ['THEHOST.com']
env.user = 'THEUSER'
env.password = 'THEPASSWORD'
def put_file(file):
put(file, './THETARGETDIRECTORY/') # it's copied into the target directory
Then run the file with the fab command:
fab -f fab_putfile.py put_file:file=./path/to/my/file
And you're done! :)