Go with LinuxMint. The Cinnamon Edition is best for a Windows user. Use the Windows Key to get started. Make sure you back up your Windows data extensively-- Mint does not upgrade Windows, it replaces Windows, so a fresh BLANK machine is the best place to start. You can also run LinuxMint in a virtual machine, or dual-boot it. Explanations of how to do this are easily found by your favorite search engine. Remember to backup 2x if you're replacing, and know that your data will need to be restored folder-by-folder (example, My Documents into (your new user name)/Documents. It's the best experience for Windows XP or 7/8x users.
You can also boot a trial of it on DVD (or flash drive if you know how) to see what it "feels" and looks like before you do an install. Get used to searching online for help, but often, you'll get direct answers if you ask the right questions. Ubuntu is my choice #2. Not as obvious, but with potentially more extensive support (in terms of sites and users). LinuxMint is based on Ubuntu, but does not have the same windowing method. What works on Ubuntu *should* work on LinuxMint, so many good software choices.