Where do I store my files such that they can be found?
First a description. The path that contains acct, cache, config, d, data, dev, mnt, proc, etc is the device's root directory. The root directory is the root of all filesystem hierarchy in an Android device.

When you connect an Android device via USB to a computer, usually via MTP in newer devices or USB Mass Storage in older devices, the root directory of Android is never exposed to the computer. But rather only a small number of directories are exposed to the computer. The directories that are exposed to computer connected to USB is the external storage. 

The path to the external storage, unfortunately, varies by device. The external storage of many Android devices points to the SD Card storage; this is not necessarily always the case, such as with devices that doesn't have SD Card, the external storage actually points to a regular folder. These are some of the locations that external storage may be in:

/mnt/extSdCard/
/mnt/external_sd
/mnt/sdcard/
/storage/emulated/0/


Many Android file browser application generally have at least two specially programmed location to open, one showing the device root and the other the external storage. Look if your file browser application shows the external storage. If your file manager don't show you your external storage by default, try downloading OI File Manager, this file manager shows your external storage by default.

Once you saved your apk there, you should be able to just tap on the APK to install it in most file manager worth its salt.