Japes->Norfair->Ship->PTAD->DP is probably the best order. The former two already have a certain amount of support outside the usual suspects (that is, us); Ship and PTAD will likely be easier to argue for due to DP's walkoff. I imagine Ship will be easier than PTAD since its hazards are unlikely to kill you.
Of course, all the stages have hurdles to clear. Japes has the DK hurdle and the Falco hurdle. Norfair has the Sonic-or-Wario-camping hurdle and the planking hurdle. PTAD has the cars-kill-you-at-60-and-are-random hurdle and the no-ledges and floor hurdle. Pirate Ship has rudder camping. DP has the walkoff hurdle, the one camping spot, and a few people claiming the center platform is a semicircle.
None of these are banworthy and all are easily shot down. What I'm saying is that all of them are prejudices that immediately flash through peoples' minds when they think about the stage; it's irritatingly hard to convince people of things like this when most will go "herp derp ur rong" and not really give you anything to argue with. They're the same tired, old arguments we keep shooting down and people keep bringing back up, and until we can put them down for good, we're going nowhere.
We can plan farther ahead when we get a few of these. (And also salvage RC/Brinstar/PS2, because eff Apex.)