The Children of Húrin question

Yes, I would say so. Every detail many not be understood (like the hints to the Sil in the LotR text) but enough to read and understand the story on its own without a problem. The book is a puts together what is in the Silmarillion and Unfinished Tales so there is nothing new. There is an introduction that I believe has some explanatory info, though it has been a couple years since I have read it so I can't remember for sure what the intro contains.

It is a standalone. That said reading the Silmarillion and all his other works is highly recommended.

I would say that of all the books on Middle Earth, Children of Hurin is the most stand-alone of the bunch, except for The Hobbit, which got them all going. The Silmarillion stands alone, but can be dry, especially at the beginning, if you haven't already read LOTR. Personally I think they should be read in this order:

The Hobbit
LOTR, and don't skip the Appendices
Children of Hurin
Silmarillion
Lost Tales

...as for giving advances about the order, I think to have been lucky to follow what seems to be the best order, if there is one:
- The Lord of the Rings;
- The Hobbit;
- The Silmarillion.
Then I read The Unfinished Tales, The Book of Lost Tales (part I, part II) and, finally, The Children of Hurin.
If one wants to understand each hint of the global situation of Middle-Earth at the time of Turin Turambar, The Silmarillion must be read before anyone other book about the First Age. Only then one can understand every single aspect of the life of the Children of Hurin...

Very good story, however. I love it.

I enjoyed it. I have read The Hobbit and LOTR, and other than some articles online that is all I have read. I had no trouble with CoH being in the First Age. There is a nice map at the back that was helpful.