I use an old derailleur crankset on my bike. I simply removed the inner and outer chainrings. A singlespeed crankset without the shaped teeth of a derailleur crankset (which are designed for easy shifting, something you don't want with an IGH) but the one I have works fine.

You might struggle to find a full chain case. I use a 'hockey stick' style chainguard, which covers the upper run of the chain only. This works fine for keeping clothing out of the chain and for preventing oil from splashing around. Other chainguards enclose the entire front chainring as well as the upper run of chain.

As for the rear hub, my housemate rides a bike with a shimano nexus 8-speed and gets on well with it. I've ridden the bike and found the gear spacing practical.

3-speeds can work great as long as they're not overgeared. Many bikes with a 3-speed hub are set so you can use 3rd gear when riding downhill. This means that second gear is too low for flat ground riding, and limits the hillclimbing ability of 1st gear. You basically don't have a level ground gear, which may be why you didn't get on with it. I set mine up so that 3rd gear is a level ground gear, with 1st and 2nd for acceleration and climbing. On steep downhill sections, you can coast. It's basically a single speed with a couple of 'bailout' gears.

The chainline can usually be adjusted slightly by rearranging the rear sprocket and the one or two spacers. A lot of sprockets are dished, so you can get further adjustment by flipping the sprocket over. You need to make sure the chainring is around the same chainline to be compatible though.