I would use the deepest of the 2 unless one just looks a better than the other.
I would use the lid as the top and see how it sounds 1st. It'll be a simple matter latter to replace the lid.
I don't use bottoms as tops ... their usually pretty plain looking.
I would build it 1st .... try it out without a soundhole. You might be surprised! It is a compromise anyway, and sometimes, loosing vibrating surface can be more harmful than adding a soundhole will be helpful. I've built each way, I really don't see a lot of difference ...... even more so if yer gonna amp it.
Quick easy build with minimal tools.
Decide on your scale length. I put bridges about 1/3 from the tail-end. Again a compromise. Putting it in the middle can make it a bit crowded to play.
Go to Lowes Hardware, or the orange one ... doesn't matter which one, and find the pre-finished hardwoods. Find a 1x2 red oak "stick" in a length that will work for your overall length.
The rest is easy. Notch holes for the neck to go thru the box. Notch the top of the neck thru section so the soundboard can move freely(leave a small "shelf" at each end to support the soundboard.) Drill holes for the tuners, cut a slot for the nut. Frets are another matter entirely, but doable.
Forget calculating for the soundhole ... about the size of a quarter is about all a cigar box needs or can afford to loose.
Matt