Assembling a home recording studio is tricky and you spend tons of money and get poor recordings. That's why I think it's really important to know how what's important and what is not in your home recording.
First, you need to establish your budget. Anything over $300 will do just fine, but I'll show you there are things you can buy and still get quality recordings if your budget is lower.
The first piece of the recording gear is the microphone, so be sure to get a quality mic. AT has pretty cool mics around $100, but you can go for NT1 or other condenser microphones. It's all about your budget. Remember to read as many reviews as you can about the mic before buying it.
Next in the recording chain is the audio interface. If you have a PC you can buy a soundcard. M-Audio products are really good, but I still recommend getting an external audio interface. It will give you more mobility and usually brings better quality to your recordings. There are plenty of audio interfaces on the market, you just need to scout the best one that fits your budget.
You'll be needing some headphones and some studio monitors for mixing your songs. Headphones are not that important, anything will do. Remember to buy a pop filter, a mic stand and some cables and connectors for your audio interface.
These are the most important things you need to buy in your home recording studio. But you can always improve your setup buying a mixer. This allows you to connect and record different instruments. You can treat the recording room with acoustic foam. This will get rid of backroung noise from outdoors and it will help you get a clear perception on the sound when you mix it. As an alternative you can make your own acoustic foam using egg crates. This worked great for me on my first home studio when I was on a really tight budget.
You can record and mix your song using free software. Plenty of them available on the internet. I recommend this home recording studio setup. You'll find there some of the best home studio products along with prices, pictures and features.