new install 3-way switch and outlet question

Took out garage door in walk-out basement, boxed it in with 2x8's and 36" walk-thru door. Before insulating, I would like to install an outlet near the new door and a 3-way light switch.

The basement was divided down the center with a concrete brick wall and walk thru door in the middle. I would like to be able to walk into the basement at the new walk thru, flip a light switch and walk over to the center door and flip the light off.

The hardware man said to bring power on a 14 gauge line to the outlet (install a GFI) and then do the 3-way from the outlet on a smaller 12 gauge line.

I've tried to get a contractor here but they are 3 months out with work and this is a small job. Also, money IS tight.

The electric box is next to the new boxed in area. Lots of wires running across the top and over to the other side of the basement. Can I install a junction box and wire into one of these wires as long as they are the same gauge? Run the new wire down to the new GFI outlet, connect the 3-way to this outlet? It would also mean a new light fixture.

I believe advise would be to wire from the electric box but I know so little and would be worried about doing that. My experience is cutting wire and installing a junction box and wiring into that.

I thought of watching a youtube video on how to wire and 3-way switch.

Thanks and hope I've described this properly.

 

So much wrong with that. #12 is larger not smaller than #14. Wire size is based on breaker size. Basement receptacles are usually on a 20 amp breaker which means #12 minimum. You can not use #14 on a 20 amp breaker.Maybe but they would have to be on a non restricted use circuit and not near their capacity for loads. Unless there is 12" of slack in the cables you would need two junction boxes a foot apart connected by a piece of cable. Simplest and best is to run a new circuit.

Run #12 NMb to your GFCI receptacle. Run #12 NM-b from the line (not load) side of the GFCI receptacle to your 3-way switch.