Mine also comes through alot of different channels. 90% of the time, it's already in my head; or once I hit the first note I get something. When I got a melody with some kind of theme to it, I think of the right instrument to play it. Sometimes on guitar, sometimes on bass, or by messing with fruityloops, or this little generic mini keyboard I have. Once I get it out, usually only a phrase or a period. I start building from there. Then like a seed, it blossoms into a flower, woohooo!! :D

Rarely do I start with a chord progression, I think in past discussions I've made my reasons clear. As for branching off someone else's tune, I try not to do that but I also won't lie and say I haven't. Sometimes I do hear something in a song and say, "wow thats cool" and it will spawn an idea of my own. If it's a very distinct idea, I usually take it and retrograde it or do some variation of it so that's it's not exactly the same.