If a bike without rack mounts is a non-starter, that's very limiting. You can always get some SS p-clamps and put a rack on most anything. Or find a good but cosmetically challenged frame and add the mounts, then powdercoat.

I'm no expert on touring frames (which generally will have the mounts), but I'm told that many of them ride best when they're loaded. It doesn't sound like that's what you have in mind for the bike, so I'd be a bit cautious with full-blown tourers.