inner hub gears are near zero maintenance, and as you don't need a thin chain, the external parts (chain, "cassette", etc) can be made fairly sturdy. They also have a nice feature for town use: you can change gear while stopped at the lights. No more anticipation or setting off in the wrong gear.
The Sturmey Archer 3 speeds are probably the most affordable to build a bike from; the ratio normally gives a good spread. If you are hoping to fit this on drop bars, then you should be able to hook up a 3-speed front-shifter/brake unit to the SA hub. I have an 1999 Sachs hub set up exactly like this; Shimano RSX road lever controlling shifting -it just goes in the opposite direction from a front ring.
For 1x8 or 1x9 at the back, that's a pretty wide spread these days; you can go better than 1:1 at the bottom, at the expense of the upper gears: you'll need to get that front ring something everyone can agree on. 8 speed is probably the best choice as it is easier to set up than 9 speed; the chains are wider and a bit stronger. Even 9sp is easier than 10-11 for the same reason.
Going for a 1x8 would probably be a lower cost option as you can get rear freehub wheels for not much expense...though once you add in the cost of wheel+cassette+derailleur there's less in it.
[Update Aug 2018] When those Sachs hubs start playing up you will discover that it's nearly impossible to get spare parts...the only reason my bike is working again is the local bike shop found a replacement activation chain in one of their boxes of "old bike bits"