Either gauge should work with no problem, but only SO cord is rated for 600v. 300v cord is SJ, but I would stick with a 600v rated insulation. Splicing in a metal box will work fine if you have good strain relief for the cords going into the box, and ground the box when you make the connections.
I haven't used an electronic ballast, but you are getting quite a ways out there for a standard ignitor on a magnetic ballast.
I haven't used an electronic ballast, but you are getting quite a ways out there for a standard ignitor on a magnetic ballast.