Loads of midi keyboards come with a free copy of Ableton lite / Fruity Loops, and usually other stuff, some of which is damned good. It's enough to get you hooked and having a laugh expressing yourself.
Cheap 25 key mini Akai's start from 80 quid, but there's usually deals on second user / open box.
Arturia Keylab Essential is a cracker, 49 full size keys and a proper quality interface, very nice at £160 odd
Or if you're not into keys, you could start with a Launchpad.
I mention them because they're all proper boys toys, with pads to drum, colorful displays, nobs, wheels, sliders.
Many obstacles to remixing old tunes have disappeared, we now have free apps like UVR, which can rip any tune into component instrument / vocal stems.