Another welcome to Home Recording.
I'd suggest you start by reading all the FAQs stickied at the top of this forum. They'll give some of the basics of computer recording.
Exactly what's best for you will depend on what you want to record and what you want to do with the finished product. However, some general guidelines would be:
What do you need? At the most basic, you need a microphone, an interface to get that microphone signal into your computer, and software on the computer to manipulate that signal. You also need ways to monitor (listen to) what you're recording and editing. For the mic and interface you'll have a choice of a standard analogue microphone and an interface box or a microphone with a USB output. The normal advice is usually to avoid USB mics because they can cause more problems than they solve--there's a FAQ about this in the microphones section.
Software? For simple recording and editing, the recommendation above for Audacity is a good one. It's free and does a good job but with limited options for what you can do. If you want more ability to alter your stuff and add fancies like reverb, compression or a who multitude of special effects, download the free trial of a software package called
Reaper. It's free to try (and the trial is unlimited) and about the cheapest bit of audio software out there ($60) when you decide to buy.
Now, one other thing. You mention MP3. While you may wish to end up on MP3 that's a lossy compressed format--every time you open a file then save it again you lower quality. You're better off to work with uncompressed wave files and only convert the finished product to MP3 when you're done working on it.
Sorry to be so general but your apparently easy question could require a huge book or two to answer fully! Read the FAQs then ask any specific questions you have!
