Thanks for your questions, Dallas.
Sounds like our book Amazon Web Services in Action is a perfect fit for you.
Dallas Gimpel wrote:
If I set up an Ubuntu VM, do I get a root account on it? Am I able to install stuff just like a physical machine sitting in my office?
Yes, you can choose an image (e.g. Ubuntu) for your virtual servers. You will then be able to login as root and install packages as needed.
Dallas Gimpel wrote:
If I don't want a public-facing server, does AWS have a VPN implementation (eg, between my office network and VM)?
Yes, it is called VPC (Virtual Private Cloud). You can spin up virtual servers in a private network on AWS. Site-to-Site-VPN or even a direct connect is also possible.
Dallas Gimpel wrote:
Once I have a VM set up the way I want it, is there a way to "clone" that configuration?
Yes, you are able to create your own images based on running virtual servers (EC2 instances).
Dallas Gimpel wrote:
Also, I'm not sure what to expect in terms of pricing. My impression is that they're fairly reasonable but can you give me a ballpark range as to what a vanilla Linux VM might run? If that's too vague, I understand.
AWS is billed per usage. So you will pay for the resources you are using (e.g. hours of running virtual server, size of objects stored on S3, ...). Estimating costs is only possible with more details about your use case. You can use the
http://calculator.s3.amazonaws.com/index.html to estimate the costs for a specific setup. But you will need some background knowledge about the AWS services before you are able to use the calculator.