Audacity is probably the most frequently used free audio editor one can find in the actual market. The software is on par with a nice amount of paying softwares and offers many useful tools for editing music or sound effects. Removing noise, cut and paste audio tracks, removing vocals from a song, applying special effects you got them!
This software is 100% freeware which means you will never reach a paywall or be annoyed by some tools on demo mode, limitations of time - other than your hard drive capacity of course - etc. Furthermore, Audacity can use extra plugins that you can find in the web, making it an even more competitive software for audio editors and music producers.
Another strength of this software is it's surprisingly easy to use user interface. It is a good thing, especially being used to have 100% freeware softwares plagued with an user interface which requires some kind of tutorial to get the hang of it.
It is possible to record through both a microphone and the computer playback system. As said above, it is really easy to set up and the option can easily be found in the user interface.
You'll be able to create soundtracks with a sample rate as high as 192000 Hz and will have the ability to create audio files at 24 bits depth.
All the necessary tools for a proper mix are there, you'll find the mandatory compressor and equalizer along some other tools. Some of these can be slightly inconsistent in terms of ease of use but this is due to the fact that Audacity is an open source project with many different people being involved in it's development.
All in all we can say that Audacity is a wonderful free tool to use for editing your soundtracks and will provide you all that you need to get a highly satisfying experience!