Your comment has really tempted me to switch to AWS from DO just to try the waters of the cloud. However, the terminology and all the different services offered by AWS are mind-boggling.
Are there any good introductions to cloud computing you could recommend?
If you're coming from running standalone servers on DO you don't need to worry about most of AWS' services.
To get the equivalent you'll need to read up on the basics of:
EC2, which provides you with the actual server.
EBS, their network attached storage which your server will boot from.
Elastic IPs, to give the server a stable public IP address you can point DNS at.
And Security Groups, which don't have a DO equivalent, but control network access to your server. They're arguably worth moving from DO for alone.
If you just want to test the waters then EC2's startup wizard will handle all this for you, and you don't really have to think much more about it than you would on DO. However, you've then got the ability to grow into the rest of AWS as you need it.
Are there any good introductions to cloud computing you could recommend?