I have one caveat for using the HCDU. It's a great tool, but keep in mind it doesn't find guaranteed conflicts. What it does is notify you of which mods will alter the same behavior and, as such,
may conflict. It's a good starting point, but just remember there will be times when what it lists work just fine together. There can also be times when it doesn't find any possible conflicts when there clearly is one.
So, if you do use the HCDU, test the mods it has listed and pull them out. If your game runs fine, then you've discovered your conflict and you'll have to pick which of the conflicting mods you want to keep and which you want to discard. If your game is still not working right, then you have a conflict you'll have to dig out via the 50/50 method.
Edit: Oh, and just as an addition, there are three subfolders I will ALWAYS have in my DL folder. One is "New" and the other is "Mods & Hacks" and the third is "Default Replacements". All new cc goes into the "New" subfolder until I know it's working fine. If some mesh ends up mucking things up, I know to look in my new stuffAll mods/hacks go into the Mods & Hacks and, because it's so easy to forget what default replacements you have, I have all my replacements in their own subfolder, for the simple reason you can only have one default replacement of each type (one for eyes, one for skin, etc). If I find a new default replacement I like better, it's easier to find the one I have and remove it.