Paul, it's tough to do preliminary research on AWS and summarize it so concisely. Best woud be to start/continue using sets of services and the nuances and "gotchas" you noted will become clearer. Particularly EC2. For example, here are some points you noted followed by --> some clarifications:

* Lots of different sizes for cpus. --> Virtual servers come in many configurations. Choose based on the combination of CPU, RAM and disk I/O required.

* Only scales down to 40 dollars a month. --> t1.micro instances are $15/month. m1.small instances are $40/month or as low as $25/month with reserved instances (amortized over 1 year) or even less than $25/month with spot instances.

* If you reboot it, the data will disappear. --> No. Data is not lost on reboot. Most instances have two types of storage: EBS and Instance Store. The Instance Store data is lost when instances are powered off. EBS and Instance Store data survives across reboots. Understanding the difference between a rebot and a power-off is important.

* Firewall is turned on by default so you can't connect to it. Have to turn that off. --> Clearer would be to say firewall ports need to be opened to support the services you need (such as SSH/RDP, HTTP, etc.).

* The name of it changes on reboot. No. The DNS name, external IP and internal AWS IP are preserved across reboots. They are lost when an instance is powered off. (See above.)

* Use the IPs which amazon gives away for free. --> AWS limits you to 5 Elastic IP addresses (for the most part). You can (for the most part) avoid using Elastic IPs by using the public DNS of the instances, often in conjunction with your own domain DNS. For example, a database server might resolve like so:

    db1.example.com (your domain)
    |-> ec2-12-34-56-789.compute-1.amazonaws.com (public AWS DNS)
        |-> 12.34.56.789 (public IP if you are outside of AWS)
        |-> 10.11.12.13 (internal AWS IP if you are inside AWS)

Enjoy the learning experience. It will take some time for it to all sink in.