I grew up in the 60’s and always wanted a bike with a Sturmey Archer hub. Back then you found them on British bikes that as kids we called English racers. I never did get an English racer, or a Sturmey Archer hub, but I got a chance to ride them a fair bit back them, and they worked well.

The clicking "freewheel" noise is normal when pedaling. This is true on 3-speed hubs like yours as well as most of those with more gears. This is because with internally geared hubs, the gears are always engaged and driving different freewheels at different speeds, and whichever one is going faster drives the hub, while the others freewheel. However, more expensive hubs like the Shimano Alfine and higher-end Nexus models will not make freewheeling noise because they use "roller clutches" which are equivalent in function to freewheels but don't make noise due to a different design principle. Also, shifting delay is normal until you ease off the pedals to allow the internal mechanisms to move to their new positions.

It's great to see all these Americans realize what a dumb fad single speeds were.