Ableton is certainly really great software for doing mashups and DJ edits, but it may be too much blasting power if you’re not looking to get into serious production (though I can’t say I know Lite). It does look like Ableton Lite is just a pack-in with particular products, so you’d probably need to buy particular hardware to get a copy of it with it.
A good place to start may be to check out How To Make Your Own DJ Edits, offered by this site – it seems like it should be a good course, though I do not have personal experience with it as I have been producing much longer than I’ve been DJing.
You might want to check out Mashup by the folks over at Mixed in Key. I don’t have direct experience with it, but it looks like a good low cost solution for mashups and DJ edits if you are not needing hardcore production software.
Live remixing is certainly a lot more work, but at the same time, it is something that really allows you a lot of expression – it is something that I want to work into my sets more.
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