Here are the methods:
Hardcore Classic - roll 3d6 and record it for each attribute. No rerolls, no putting rolls where you want them.
Classic - roll 3d6 six time and assign them to attributes as you wish.
Standard - roll 4d6, discard lowest die, do it six times and assign as you see fit. (Possible hardcore variant would be to assign them as you roll)
Heroic - roll 2d6 and add 6, again do it six times, etc, etc.
When responding I'd also like to hear your reasoning for liking it. Maybe there's something in your reasoning I never thought of.