Welcome aboard
I would recommend at least 3/16" if not 1/4" plywood for the bulkheads, anything less is likely to twist/bend. Keel 3/8" to 1/2" plywood. As to kit or scratch, my first was a scratch built plank on frame Brittany Trawler which came out OK. Not Gold Medal winner but I like it. However, if you feel the need for a kit go for it. You would need to pick one that uses the same technique you want to use on your Mayflower.
HTH
Doug