I've never used a virtual machine, but I'd to start..
What's the easiest setup in terms of software and operating system? What's free? Any tips for someone completely new to the virtual machine scene?
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Well, Oracle VirtualBox has a free version that runs Windows, Linux etc. and free for non-commercial use. It's pretty easy to start with, too.
UPDATE 2014: Unfortunately, one core developer on VirtualBox team decided to screw up compatibility and basic functionality in favor of trying to secure guest OS from the malware on the host (which is outright impossible), and since version 4.3.14 it's unusable (works very slow, causes blue screens on host machine or does not run at all)
Either use VirtualBox 4.3.12 or use Hyper-V which comes free with Windows 8 (you have to enable it in Windows Features box).
I personally really like VirtualBox, especially since I can install it directly from the Ubuntu repositories. but whichever one you choose will probably come down to which you need. If you plan on migrating instances to Amazon's EC2 for example, Xen would be your favorite. There's also VMWare player, which is free, and an upgraded version that isn't.
Play around with several, and get the feel for them. (But not at the same time on the same host; I'm sure they don't play well together, because they all access the low-level stuff of the host.)