You don't neccessarily need any special hardware to multitrack. However, a decent audio interface would help in terms of performance and quality. But then that applies to recording anything with a computer really.
If you want to record multiple tracks at the same time,
then you'd need some kind of multi-input audio interface to suit those needs. But if that's not the case, it's only really only the requirement for multitrackng software that's vital.
For software, I'd recommend checking out Reaper. It's on an unlimited trail I think, but if you like it, it's well worth the $40 (or whatever it is, not that much money compared to the likes of Cubase etc anyway, and has a similar level of functionality).
Check out
http://www.reaper.fm
And yes, with most of that type of software you can manipulate the hell out of each individual track....you can cut, slice, stretch and bend the audio to your hearts content with the editors in the software, and thanks to the wonders of non-destructive editing, it will generally leave your original audio file intact. You can also add EQ, effects etc etc, using plugins. Generally, recording software comes with some stock plugins. Some good, some not. You can also buy a lot of plugins, and there are some really good freeware plugs out there too. You can find a lot of plugins, from free to expensive as hell, at
http://www.kvraudio.com
