The most common, free, and overlooked software of today's music market would be Apple's Garageband.
Hold it; Most of you would think it sucks and doesn't do much.
First, you may want an Apple Computer, which are very decent for media production (Let's not start an argument over what is better between Apple and PC. It depends on your choices). This could be costly, but it's a step you want to take towards music production.
GarageBand ships with HUNDREDS of presets for Software Instruments and Real instruments, and even a ton of audio effects. The guys at Apple even made them sound very nice. For anyone who is novice, GB would be a lot of fun, and it would sound great.
GB is great for recording and studio on the go too. Paired with an Apple laptop (iBook, MacBook, or PowerBook), you can do some fairly amazing things on the go. In fact, this software is so good that if you do decide to continue into the music field, throwing money at GB will actually expand your potential with just this simple yet free software.
If you horrendously hate GB and Apple, or don't want to get one, you can always try Audacity, which I believe is free for use at the moment. It too, is a software of decency. Though it won't measure up to 1000$ softwares, it's a good place to start.
Of course, the common thing in the Music fields is: The more money you throw at it, the better you get yourself. If you want to play for fun, you'l want to spend anywhere from a few hundred dollars to 5000$ for gear, monitors, a MIDI controller, etc. There's no "cheap way" to play music. It's going to be costly.
As a professional musician, I am anti-piracy by heart. However, I strongly dislike corporate scheming; the inredible price amateurs have to pay for quality software seems ridiculous. Cubase sells upward to 700 - 800$. Pro Tools, Logic, sometimes get close to 1000$ after hardware and software set up, not including specific computer components and internal soundcards. It's just not reasonable for low-budget individuals.
Take your time, start out slow and small. Invest carefully, and mak esure you do your research.