After playing for a while, this is my general thoughts:
Neutral Starters
All of these stages have little to no hazards with decent sizes for 1v1 play and few situations where the stage becomes too obstructive (walls and ceilings),
Battlefield - Standard
Final Destination and all Omega Stages - Standard
Kongo Jungle 64 - Big blast zones and a barrel under the stage, but otherwise a very neutral stage.
Lylat Cruise - Slanted sides and dat lip, but otherwise a fine stage.
Smashville - FD with a floating platform.
Town and City - FD with lots of floating platforms.
Duck Hunt - FD with a few tiny stationary platforms, and a dog!
Counterpicks
These stages are close to being completely competitive, but may have minor stage hazards, small obstructive pieces of the environment, or various stage transitions.
Halberd - Retardedly easy hazards.
Delfino Plaza - No hazards, but has water elements and a few walls and walk-offs. Nothing permanent or major.
Skyloft - Like delfino plaza, there's a few stage elements that are a hindrance, but they don't last long and is otherwise a fine stage. Things of note are the recovery-hurting waterfalls, but you'd need to be hit down there to really have it affect you for the 10 seconds that transition is there. Also, there are some rare moments while flying around that a piece of the landscape can hit a player for minor damage and send them flying back in the other direction. These moments are rare and are only available for a split second. I spiked Luigi right into one, preventing him from dying. Feels more like Brinstar Acid than a full-on stage kill. I still feel this stage is counterpick-worthy despite all this. After all, if Halberd and it's hazards are legal, the minor hazards here should be no trouble at all.
Castle Siege - Only the 2nd transition is the place that turns this from a neutral to a counterpick. The statues and walk-offs, but they're not major.
Wuhu Island - There's water elements no different than delfino. The only true hazardous and questionable parts are the speedboat that kills similarly to Pirate Ship's from Brawl (and faster), as well as the beach, which is massive. However, transitions last only 10-12 seconds each and most of the stage is harmless with tons of variety. Also, the boat really only harms people with a bad horizontal recovery since they need to recover straight up and down, though if they land in the water far enough away, they can recover without worry.
Pilotwings - Sometimes there's a wall element and a short freefall element, but otherwise a harmless tilting stage.
Questionable
These are stages that I believe have the potential to be made into counterpicks, but there are some instances in the stage that can really screw things up, whether it's certain hazards, stage obstructions, or other problems.
Mushroom Kingdom U - The hazards and stage transitions honestly are not bad. However, there is one thing about this stage that turns it from a possible counterpick to something more debatable: Nabbit. Though mash the buttons enough and you'll escape just fine, he's just there to be a pest with a chance of actually killing someone. He's easy to kill and against good players, he probably wont have a chance at grabbing anyone, let alone killing anyone. The icicles and blowfish are stupid easy to avoid though, unless you get the secret surprise blowfish pop-up from underneath.
Pokemon Stadium 2 - The only thing truly bad about this stage are the transitions that mess with the physics of the stage, whether you're slipping around or floating, or jumping over treadmills.
Possible, but should be banned
These are stages that have a lot of the elements to be a legal stage, but has either one or more major problems that ruin the entire thing.
Big Battlefield - Just too big for 1v1. Even too big for teams.
Mario Circuit - Almost considered this a counterpick, but then I examined it more closely. Cars aren't NEARLY as deadly as Port Town's and are easily dodged, but the fact they're even there means that they could ruin the flow. Also, there is a single moment where, if timed perfectly, you can kill an opponent by throwing them up into the ceiling as the stage begins it's transition to lock them into an instant-death situation.
Luigi's Mansion - Ceiling shenanigans.
Kalos Pokemon League - Lots of hazards, but many of them are easily avoidable, but the fact there's so many make this place likely to be banned, but still something worth discussing. But with all the other possible stages, it's not worth it. The sword portion is what makes this most likely to be banned rather than 'questionable.'
-Windy Hill Zone - Huge, but the biggest problem are the springs on the sides. Otherwise it's just big.
Definitely should be banned
Everything else.