Re: thinking bout an 8 spd sturmy
The biggest problem with the 8-speed Sturmey is that gears 2-8 are all internally overdriven. 1st gear is 1:1 as opposed to 2nd gear for the 3-speed and 3rd gear for the 5-speed. This means that the 8-speed Sturmey wouldn't offer any hillclimbing benefits over the 3-speed you currently have unless you re-gear the cranks.
The Sturmey 3 and 5-speeds have proven themselves to be up to the task of motorvation. You might consider the 5 as it has 2 gears below 1:1.