OK 1000w will need that #4 to the battery.
If you want the existing outlet to work you can wire the inverter power to that circuit using a transfer switch. I recommend the 15 amp Xantrex.
Transfer switch has two input, one output. (1)Remove the branch circuit romex from the power center and connect to the output of the transfer switch. That is all three Hot, Neutral and Ground. (2) connect the inverter to the default (normally closed) input. (3) New piece of romex from the panel to the other transfer switch input. Connect in the panel same as the original was removed.
s/b straight forward if you have done any home wiring.
http://www.bestconverter.com/Xantrex-Prowatt-SW-Inline-15-Amp-Transfer-Switch_p_457.htmlIf the branch circuit powers items not wanted to run from the inverter, such as 120v fridge, those items need to be off or disconnected.
Some inverters will not tolerate getting wired into a system and sharing the 120v ground with the battery negative. If this is the case you get to just run an extension cord direct.