Among others I tried Solid Explorer, X-plore, FX File Explorer, and ES3. These are all the big guys, full set of functions for power users. Which to chose is mostly a matter of personal preference, reflected by all of them getting a 4.7 rating at Google Play. My personal favourite yet is FX File Explorer, bcs I like the interface, and also that it only requires few permissions. Albeit I personally do not need changeable skins, themes and surround sound in a File Manager.
For everyone who likes a simple, clean and fast File browser OI type, take a look at File Explorer by Amey Sakhadeo (there are several named File Explorer in the market, check for the developer name). It is of humble size, and uses minimum system resources. It only requires 3 permissions, needed for its function. It's like a more modern OI File Manger. I would like to see an exit button which removes it immediately from system memory.
Something similar but with root support is the Inka File Manger. Nice are the two side bars to access settings. It has an Exit button but it's not removed from system memory through it.