Unless you fancy trying your luck persuading a record label to let you remix one of their tracks, you'll be very lucky to get hold of raw audio for anything. Having said that acapellas can be found fairly easily.
If you want something to get you started, check out
http://www.realworldremixed.com
I doubt you will have heard many of the tracks on there BUT they do give you the full raw audio package. Great for chucking into your chosen DAW and having a play with.
For all production/remixing/etc the three main ones are Pro Tools, Cubase and Logic. I use Cubase (When I get a mac pro I'll be switching to Logic). For DJ'ing it's Ableton or Tracktor. I use Ableton. Virtual DJ is good, quite basic and ideal for a beginner but I actually started with fruity loops.
Ableton is a fantastic piece of software but if don't have experience, it will take a while for you to get up to speed.
BTW all I have mentioned above are available through less than legal channels in the same way you would get films/music.