The installation of most modern Linux distributions is fairly bulletproof at this point, even for beginners. I'd start with something mainstream like Linux Mint (the current version, 17, is a long term service release which is a plus for a beginner). I don't care much for Ubuntu's Unity interface, but it is also a popular option if you want to try it. The one downside to Mint for beginners is the inability to easily upgrade a system in place to a new release in lieu of doing a complete wipe and install.
The best thing about Linux is that it is free - you can try 100 different distros and pick the one you like. As others have pointed out,
www.distrowatch.com is a good place to start.
If you want to go the Windows route, you can always download the
90 day Windows trial version from the Microsoft website. At the end of 90 days, you can extend the trial a few more months using "slmgr /rearm" command from a command prompt before it finally runs out. The downside of using the trial version is that you would have to do a total system reinstall either when the trial runs out or when you get your own copy of Windows for your new machine.