I am installing a projector in my home and I would like to move my existing power outlet about 10 feet. I would like to run the wire behind the wall to keep things looking nice. I am not an electrician, but I have done some basic home electrical work such as replacing outlets and I installed a new dishwasher (where none previously existed) which meant I had to run wires into the basement and manage my circuit breakers.
Essentially, I want to make sure I am not doing something stupid when I:
1. Get a solid wire set (with ground) with enough capacity for the items that will be plugged in (12 or 10 gauge -- bigger is better)
2. Either connect (gang) the new wire to the existing outlet OR remove the old outlet completely and connect the new wiring to the old using screw-on wire connectors. Note that the house is very old, and the existing wiring has a black fabric casing.
3. Run the new wire to the desired location. (Do I need a channel for this?)
4. Connect and install new outlet.
This seems straight forward and simple enough for me to do. However I like my house and I want to prevent fires. Is there anything that I need to keep in mind while doing this, or anything that I should not do?