Might I suggest buying a very cheap bike at a thrift store just to try it out? You have a lot of ideas but (it seems to me) not so much information informing them.

Not clear on why the "look" f a rear derailleur would be an issue, but it is if it is. That leaves you pretty much with IGH.

I bet you could find a lot of cheap bikes with three-speed rear hubs in decent shape, and since you are mechanically inclined ... get three and build two from the parts.

if you don't ride a lot or ride hard, even a big-box store bike might work just fine. They tend to be cheaply made, but that isn't an issue if you don't stress them hard.

Got to places like Nashbar.com or even BikesDirect and get a feel for what is on the market. or, if you are really ready to buy a bike which might never work right---or might---go to Craigslist. if you are handy with some tools, there is plenty of readily available information on how to repair anything .....

And unless you have a lot of hills, a single-speed is fine. But from what you say, it sounds like a cheap three-speed IGH bike is what you would like best.

Good luck whatever ....