in my opinion I say insulated all the way the 1/2 will take a while to get hot and at some point is going to give up heat to the atmosphere. Prolly is better than 1/4 but it will be heavey and last longer. Post pics of your insulated box I am going to build a couple, they are highly favored by a lot of people. 1/2 plate is very expensive!!!!!!
Also should say that the challenge for me was how I wanted to attach the box. The way I "frenched" it in led me to insulate and skin after it was attached to the chamber. It would have been much easier to attach it jambo style.
I really wanted a backwoods and an offset, so I built a nice compromise.
Digging this post back up - Im currently building my smoker FB and BP out of 3/4" plate - I know, I know but it's "free" - I will let you know how it comes out - Its pretty time consuming actually (but it does free up the mind after a long day) - only getting about three or four pieces cut a night after work, but at least its moving forward -