First let me address your concern about claims that Shia hadith books are not reliable. Quiet conversely, Shia hadiths are generally more reliable for some reasons among which are these two:

* Shia believes in the [Isma](https://en.wikipedia.org/wiki/Ismah) of their twelve Imams (a.s), and have received the authentic hadiths of the Prophet of Islam (PBUH) from the Imams for more than 250 years after the Prophet of Islam passed away. Note that this period (the first 100 years after the death of the Prophet of Islam) was exactly a time that most of the falsifications in hadiths occurred, because of the political issues, and also the prohibition of writing hadiths during Umar(a.s) period.

* Generally, Shia more than all other branches of Islam emphasizes on reason and philosophy. This is why most of the Muslim philosophers were Shia.

Now, there are [four well-known books of Shia hadith](http://en.wikipedia.org/wiki/The_Four_Books) that you may know them :

* [Kitab al-Kafi](http://en.wikipedia.org/wiki/Kitab_al-Kafi) 

* [Man la yahduruhu al-Faqih](http://en.wikipedia.org/wiki/Man_la_yahduruhu_al-Faqih)

* [Tahdhib al-Ahkam](http://en.wikipedia.org/wiki/Tahdhib_al-Ahkam)

* [Al-Istibsar](http://en.wikipedia.org/wiki/Al-Istibsar)

Among these probably the most important, and also reliable is the first one, al-Kafi. This is an old book and is written a few decades after the last Shia Imam, so the falsifications at the time of writing the book were minimal. But, in recent decades, there are some efforts to analyze this book trying to separate historically weaker ones. One of the outcomes is the book **Sahih al-Kafi** (meaning the correct of al-Kafi). This book has collected the most reliable hadiths of the original al-Kafi.