The current Sturmey Archer 5 speed should be useful. the ratios of the 3 speed
are the middle 3, 1 & 5 are an even wider ratio set, above and below.
advantage practically, is the ability to shift while stopped, or nearly so.

and the sequence of the shift is sequential 12345.

if you get a 3/32" thick hub cog, [vs 1/8th] it is possible to also use 2 chainrings.
and a spring chain tensioner, & front derailleur.. [6,7,8 speed chain]

To spread put the range, big difference, or half step the 5,
with 2 chainrings pretty close together.. 3 or 4 tooth difference ..