Mostly incorrect
It depends on the license, but at least with the GPL (what the Linux kernel and most of the standard Linux tools are released under) you need to distribute the source with the binaries and the users are allowed to redistribute it. The author can charge for it, but then the person who buys it can just give it away to everyone for free, put it up on the Internet for free download, etc. so there's no realistic way to require anyone who uses it to pay for it. Other licenses are more permissive and it could be possible to keep things more closed.
The choices really aren't overwhelming... if you're looking for a general desktop distro, that rules out most of the distros right there. There's a handful of major desktop distros, and if it's a newbie not looking for a bleeding edge rolling distro or a source-based distro, that leaves a handful of choices. The best part is that you can't go *wrong* with any of those choices, and provided you've got a separate home partition, it can be easy to change later on.
