Yes, Ubuntu 14.04 x64 should be fine, just make sure it is x64.
Technically speaking, a hostname is:
a hostname is a specific name pointing to a specific host. It doesn't matter if its 1, 2, 3 or even 63 levels deep. A hostname could be bob, bob.com, bob.bobsdomain.com, bob.accounting.bobsemployer.com and so on. The point is that its a name used to refer to a specific host. If someone has their own network setup with their own private domain to use for it, then they can make a hostname be something as simple as just 'bob' if they want and that can could be considered fully qualified.
But for your purposes it will probably be an IP address.
Fill in the “Host Name (or IP address)” field with the Droplet IP address from the welcome email, make sure the port number is 22, and the connection type is SSH.
PuTTY will be fine. Just follow the instructions from here:
https://www.digitalocean.com/community/tutorials/how-to-create-your-first-digitalocean-droplet-virtual-server