Big caveat. I am not a skilled luthier. So far I have made one solid body and its not finished yet. So bear that in mind.
Having said that I reckon the easiest and probably best way to do a body is to rough shape it with a band saw and fine tune the shape with a template, a router, and ball bearing guided bits. It's good for evenly rounding corners as well. However that's an expenditure in tools that easily, even vastly, exceeds the cost of the kit, so unless you are planning on doing lots of high end woodworking or your family is in the billionaire category you'll want an alternative.
I have become a big fan of wood rasps. Previously a tool I had little use for I bought a couple of cheap Chinese made rasps when I had to shape a neck, and I'm converted. Possibly even better, but which I don't have experience of, is a Japanese design tool I think called a saw rasp. They get good press. Either way I suggest getting the body thereabouts with whatever saw is handy, getting it right down to shape with a hand rasp, and then sand. For sanding drum and /or flap wheel attachments for a power drill can assist with the horrible end grain.
An idea that came up recently is to print the body shape on a laser printer, and then use a hot iron to iron some of the toner onto the body as a guide. Do that top and bottom and it seems to me it should help getting the sides parallel. The other thing I really recommend is a small modellers square. You can get stainless steel ones at moderate cost.