You need to add C:\Python27 to your system PATH variable, not a new variable named "python".

Find the system PATH environment variable, and append to it a ; (which is the delimiter) and the path to the directory containing python.exe (e.g. C:\Python27). See below for exact steps.

The PATH environment variable lists all the locations that Windows (and cmd.exe) will check when given the name of a command, e.g. "python" (it also uses the PATHEXT variable for a list of executable file extensions to try). The first executable file it finds on the PATH with that name is the one it starts.

Note that after changing this variable, there is no need to restart Windows, but only new instances of cmd.exe will have the updated PATH. You can type set PATH at the command prompt to see what the current value is.

Exact steps for adding Python to the path on Windows 7+:

1. Computer -> System Properties (or Win+Break) -> Advanced System Settings
2. Click the Environment variables... button (in the Advanced tab)
3. Edit PATH and append ;C:\Python27 to the end (substitute your Python version)
4. Click OK. Note that changes to the PATH are only reflected in command prompts opened after the change took place.

Given that you're most familiar with Unix, I'm not sure if you are comfortable with Regedit and the Windows registry.

So let's get you a simple well-regarded tool to handle this task without asking you to manually edit the Windows registry.

First download FileTypesMan from NirSoft. It's written by Nir Sofer, who is a well-known and trusted developer. It's not open-source (unfortunately), but Nir has been publishing free tools for over 15 years with an unblemished record.

Now follow these simple steps within FileTypesMan:

1. Find the .py file type in the top pane and click on it.
2. In the bottom pane, find the open action (Name column) and double-click it.
3. In the ensuing dialog box, change the command line to "C:\Windows\py.exe" "%1"
4. In that same dialog box, ensure the Default Action checkbox is checked and the Disabled checkbox is not checked, then click OK to close the dialog box.

Voilà. You're done.

You can now close FileTypesMan.

Depending on the installed version of Windows, you may need to restart the shell. If you don't know how to do that programmatically, just log off, and log back in. Or, if you prefer, reboot.

As Gerhard mentioned in the comments, there is a significant security risk to allowing scripts to run directly like this, but you mentioned you understand the risks and the tradeoffs are worth it to you. I simply recap those comments here in this answer to help people in the future in the event that the comments get deleted.