I want to make it hard for users on a domain to access things like System Properties. Is there a way I can disable things like right clicking the start menu, accessing System Properties, and any other administrative task that regular users don't need access to?
You can disable access to this feature with a GPO.
Here's an excellent resource for GPO: http://www.petri.co.il/download_gpo_reference.htm
This is actually a reference ebook about almost all settings available through GPO. The one you're actually searching for is called "Context menu" and it's located either in Internet Explorer settings or Windows Explorer settings.
Group Policy is definitely the way to go with this. But when you're looking for the appropriate settings, don't try to think about disabling specific user actions like right-clicking My Computer. Think about the actual target areas you want to be off-limits, like the System Properties dialog. There are multiple ways to get places within Windows (mouse, keyboard shortcuts, cmd line, custom code, etc). You want to lock out the sensitive areas, not worry about locking out all the ways to get there.