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Follow How To Use SSH Keys with PuTTY on DigitalOcean Droplets (Windows users).
Then, spin up a new Ubuntu 12.04 droplet (preferably 1GB+ since you’re going run a desktop environment), and follow these tutorials to configure your it:
Finally, make sure you disable SSH password login (you will only be able to use your SSH key to log in, which is much more secure):
sudo sed -i 's/PermitRootLogin yes/PermitRootLogin without-password/' /etc/ssh/sshd_config
sudo service ssh restart
http://prntscr.com/44mcl3 looks like an error on your end. I’m not sure what might be causing it, but try googling it.
Let us know how it goes! :)