You won't need an expensive microphone if you're recording voice only. Most music stores carry a wide range of cheap microphones.
To record an MP3, you will need a computer that has some sort of audio input. If you have a Macintosh, audio input is already built into the computer and operating system. Just go to system preferences, select sound and audio input, then select the line in for your microphone. On other laptops, you may need a USB audio input device to connect your microphone into your computer. Using a USB input device will give you better sound quality, so even if you are on a Mac, this is recommended.
You will then need software to record your MP3. On a Macintosh, this software is included with the Garage Band software, which is bundled with the iLife suite. Garage Band is simple to use, and has built-in instructions to help you record your MP3. On Windows or Linux, you can use free Audacity software. You will need to download LAME, another free software, to add on the MP3 export function in Audacity.