I bought a cheapo coaster brake wheel with a generic alloy rim for less than $20. Trued and tightened the spokes and it's been fine. It's mounted on my old MTB, currently 38/14 gearing. I kept the front cantilever brake because I just can't reconcile with the notion of rear brake only (though it does a fine job). I've had some cheap steel 3" rise bars on it, but currently it has some Wald North Road bars. This bike has been through the ringer several times and looks it... scratches, patches of rust, dings... but has been a reliable workbike for almost ten years.

The biggest obstacle to going coaster brake is that the rear dropout spacing is 135mm. Coaster brake hubs are much narrower than that. I think 110mm. Fortunately, it had a extra long axle, and I was able to borrow some nuts to use as spacers. This also may affect chainline depending on what kind of sprocket you want to run.

Doesn't really matter if you use a road or MTB frame (or cantilever frame for that matter, since you'll have a bike on par with the average beach cruiser). I used a MTB frame because that's what I had. If you go with found parts, this can be very cheap. After you have a rear wheel built, the rest will be gravy. You can put it together any way you like. Match and mismatch parts. Come up with something interesting.