Does it need to be free?
If so, give this kristal try:
If you have enough spare cash, Reaper is amazing...it's worth several times the $60 price. There's also a full-featured 30-day trial:
Both of those would fit best into the home recording/general editing sections. Generally remixing uses rather different programs, though you can certainly use standard DAW programs to do it.
If you're serious about this, willing to use linux, and willing to learn a rather complex system (JACK), Ubuntu Studio rivals just about any professional software suite, and in some cases surpasses them. It's capable of hard
real-time operation, which is impossible in Windows and OS/X based machines. It will do everything you want, and then some.