Wi-Fi Network only appears after I connect to another Wi-Fi network
The first part is for testing.

You need to use the terminal and manually connect to it.

Turn On

networksetup -setairportpower en0 on


Find (you can skip this if you already know the Name)

/System/Library/PrivateFrameworks/Apple80211.framework/Versions/A/Resources/airport scan


Connect

networksetup -setairportnetwork en0 WIFI_SSID_I_WANT_TO_JOIN WIFI_PASSWORD


Enter/replace your WiFi name and password in the above.

This should have connected you to your Network.


In your Network settings your home network should be in the top of the list. 
Open your router settings and change the network name to test if problem with naming. While in Router setting, change the channel to #5 (usually the least crowded one) to eliminate interferences.
Finally, run WiFi diagnostics, by holding the "alt" key and clicking on the WiFi icon, then selecting the WiFi Diagnostics.