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Accepted Answer
The $5 dollar droplets (I’d imagine) should be fine for this purpose. It’s possible to “resize” the droplet later on if you need to.
Ubuntu is probably the most popular choice and common place to begin at if you’re new to Linux servers.
So: https://cloud.digitalocean.com/droplets/new?i=cda637&size=512mb®ion=nyc1
Also it’s always a good idea to learn and work through this guide on your new Ubuntu droplets (it has some very important groundwork in it):
Initial Server Setup with Ubuntu 16.04
Best of luck.