I'm getting a little confused. I've been handed a lot of info. So to do the half lap by hand, minimally I just need a crosscut saw and a good set of chisels?
Yes and in my opinion I wouldn't buy a whole set of chisels if costs are a consideration. I like buying great chisels one at a time. I especially like the Rob Cosman IBC chisel. The handle unscrews and the bottom of the chisel is perfectly flat all the way to the end of the threads. Also the chisel is tapered in such a way that the cutting edge is the widest point. That way the sides are less likely to bruise your work. They're around 75 bucks each but I never needed a whole set. For me it's always two or three with only two being used most of the time.