Some advantages are
1. Safety. Linux is designed to be more secure than Windows. It's difficult to make malware for Linux and no-one seems to attempt it. No worrying about viruses.
2. Convenience. A Linux distribution consists of Linux and a large bundle of software. A few programs will come on the installation disk, and the rest are in the on-line repository. No more searching the internet for a free or cheap program. You can get everything from one place, so running an update will get the bug and security fixes for all the software in one go. Have a look at the sort of things you can use:
3. Adaptability. A lot of people have said that they dislike the user interface of Windows 8. Well, hard luck, they're stuck with it. Linux has a variety of user interfaces: big, small, plain, fancy:
4. Reliability. Windows tends to deteriorate over time: the file system fragments and registry ties itself in knots. Linux just keeps on going.
5. Support. Look at all the expert advice being given here, then think of the Microsoft helpline where some underpayed clerk may well end up suggesting you re-install.
So, what to try. As Snowpine said, we need to know how much memory your computer has. Some distros will squeeze into 128MG, some really need 2GB to run at their best. One catch may be your printer. A few makes just don't get supported, like cheap Lexmarks. You can read about distributions at distrowatch, which has links to their websites and to reviews. There's a review section here: I review almost everything that comes out. Currently, two of the best for a beginner with a reasonably sized computer (preferably 1GB) are Linux Mint and PCLinuxOS.