WPA PSK and WPA Personal is the same. They just call the same thing with different names.
Why is the process so convoluted ? It's a very simple request, you'd think it would be an obvious Option like
Make Network Secure-Enabled ? yes/no;
Once you have chosen WPA with preshared key it is that simple. You just enter the passphrase. Historically you just have WEP as well. That's why there is WEP as well. And for larger enterprise setups you use RADIUS server authentication. That's why you find "WPA Enterprise" or "WPA RADIUS" (which are the same thing again). If you used WEP it would be more complicated.
Obviously your computer gets kicked out the moment you set the WPA passphrase because your computer does not know the passphrase and with passphrase in place only computers which know the passphrase are supposed to connect. You have to reconnect to your protected network. Remove the network from the list of preferred networks. Then search for available networks again, pick your network and the computer should automatically ask for the passphrase and then you are in.