bx wire problems

i wanted to move some switches, the house is bx cable or armored cable whatever you prefer. it was built in the 60's and the wires are white/black, or for the 3-ways, white/black/red. it has the aluminum strip that wraps around the metal sheathing that serves as the "ground". the breaker box is grounded to the water pipe in the basement. i havent had a ton of experience with a/c cable mostly just romex. My question is how to extend the wire? can i use romex or mc cable with the green ground wire? metal or plastic boxes? through books online and other diy help, i have heard use the mc cable and metal boxes, connect black to black white to white and the green ground wire to the metal box with a screw? thanks for your help and input!!
p.s. or should i try to find the ac cable with the bonding wire? seems hard to come by.

with matching wire - your right white to white - etc.

Metal bax is not necessary, there is always a ground juntion.

And the joints wire to wire need wire marrets.
And as for wire - if its in the house, you dont need armoured. Just make sure the wire is rated for the breaker in amps.