Actually I place the battery in a backpack if you like you can go for a 2Ah battery it will fit in your box and you should still get 8 hours out of it depending on coil and battery condition I use this 7Ah battery because it was readily available and two I don't have to worry about charging it when out for along weekend.
So this is really just up to you also you will see that the price is not very different between the 7Ah and the 2Ah. Don't use wire from an old transformer for your coil the insulation will have small cracks in it and could cause you lots of problems rather get 50m of magnet wire to wind it.
Regards Xavier
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Xavier