I would say 3/8 to 1/2" as well. To start out I would first practice cutting straight and to a line. So mark the depth on a piece of squared off scrap, put it in your vise and just cut down straight to the line. Check all faces with a square to see how you did. Do this until you can consistently stop before the line and cut straight down.
For your first dovetails poplar is about the most forgiving. You would think pine would be easier but it tears out so bad. You really need sharp chisels
. Not that pine is awful to start out with. You could use that as well.
I know you are primarily a hand tool user which means prepping square "scraps" is a little bit of work. If you want some come on over and we will joint/plane some real quick.
And don't feel bad if it takes you longer than Rob Cosman
. It takes me 30 minutes to do the same job he does in 3! (not that I am any good at this either).
Oh and for a good project how about a cabinet for your hand tools?
Salem